January 23, Week 2 Today: Chapter 2, Instantaneous Velocity and - - PowerPoint PPT Presentation

Velocity January 23, 2013 - p. 1/12

January 23, Week 2

Today: Chapter 2, Instantaneous Velocity and Accleration Homework Assignment #2 - Due January 25

Mastering Physics: 6 problems from chapters 1 and 2. Written Question: 2.75

Box numbers will be posted online tomorrow morning Friday office hours will be held in Regener Hall 114

Velocity January 23, 2013 - p. 2/12

Review

Position, x: - How far and what direction from origin x

Velocity January 23, 2013 - p. 2/12

Review

Position, x: - How far and what direction from origin x Displacement, ∆x = x2 − x1 - Change in Position

Velocity January 23, 2013 - p. 2/12

Review

Position, x: - How far and what direction from origin x Displacement, ∆x = x2 − x1 - Change in Position Distance, d - how far from initial to final position, always positive

Velocity January 23, 2013 - p. 2/12

Review

Position, x: - How far and what direction from origin x Displacement, ∆x = x2 − x1 - Change in Position Distance, d - how far from initial to final position, always positive Average Speed: spav = d ∆t

Velocity January 23, 2013 - p. 2/12

Review

Position, x: - How far and what direction from origin x Displacement, ∆x = x2 − x1 - Change in Position Distance, d - how far from initial to final position, always positive Average Speed: spav = d ∆t Average Velocity: vav = ∆x ∆t = x2 − x1 t2 − t1 unit: m/s

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.)

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.) (a) #1, #2, #3

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.) (a) #1, #2, #3 (b) #1, #3, #2

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.) (a) #1, #2, #3 (b) #1, #3, #2 (c) #3, #1, #2

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.) (a) #1, #2, #3 (b) #1, #3, #2 (c) #3, #1, #2 (d) #3, #2, #1

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.) (a) #1, #2, #3 (b) #1, #3, #2 (c) #3, #1, #2 (d) #3, #2, #1 (e) #2, #1, #3

Velocity January 23, 2013 - p. 3/12

Average Velocity Exercise

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Which of the following is the correct ranking of the cars’ average velocities from smallest to largest? (Use the usual sign convention and put negative numbers first.) (a) #1, #2, #3 (b) #1, #3, #2 (c) #3, #1, #2 (d) #3, #2, #1 (e) #2, #1, #3

Velocity January 23, 2013 - p. 4/12

Velocity Exercise Followup

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute.

Velocity January 23, 2013 - p. 4/12

Velocity Exercise Followup

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Car #1: vav = 15 m/s

Velocity January 23, 2013 - p. 4/12

Velocity Exercise Followup

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Car #1: vav = 15 m/s Car #2: It travels (10 m/s)(5 s) = 50 m to the right and then (25 m/s)(2 s) = 50 m to the left. Its displacement for the entire trip is 0 ⇒ vav = 0

Velocity January 23, 2013 - p. 4/12

Velocity Exercise Followup

Consider three cars which perform the following motions: Car #1 travels to the right at 15 m/s. Car #2 goes to the right for 5 s at 10 m/s, immediately turns around, and goes to the left at 25 m/s for 2 s. Car #3 travels 90 m to the left every minute. Car #1: vav = 15 m/s Car #2: It travels (10 m/s)(5 s) = 50 m to the right and then (25 m/s)(2 s) = 50 m to the left. Its displacement for the entire trip is 0 ⇒ vav = 0 Car #3: vav = −90 m 1 min = −90 m 60 s = −1.5 m/s

Velocity January 23, 2013 - p. 5/12

Significant Figures

■ Significant Figures = express the accuracy of a

measurement.

Velocity January 23, 2013 - p. 5/12

Significant Figures

■ Significant Figures = express the accuracy of a

measurement.

■ Usually just the number of digits you see in the number.

Velocity January 23, 2013 - p. 5/12

Significant Figures

■ Significant Figures = express the accuracy of a

measurement.

■ Usually just the number of digits you see in the number. ■ Exceptions: ◆ Strings of zeros at the end of large numbers or at the

beginning of small numbers are not significant.

◆ Zeroes at the end of all numbers are significant.

Velocity January 23, 2013 - p. 5/12

Significant Figures

■ Significant Figures = express the accuracy of a

measurement.

■ Usually just the number of digits you see in the number. ■ Exceptions: ◆ Strings of zeros at the end of large numbers or at the

beginning of small numbers are not significant.

◆ Zeroes at the end of all numbers are significant. ■ When multiplying or dividing, we round to the fewest number

• f significant figures.

Velocity January 23, 2013 - p. 5/12

Significant Figures

■ Significant Figures = express the accuracy of a

measurement.

■ Usually just the number of digits you see in the number. ■ Exceptions: ◆ Strings of zeros at the end of large numbers or at the

beginning of small numbers are not significant.

◆ Zeroes at the end of all numbers are significant. ■ When multiplying or dividing, we round to the fewest number

• f significant figures.

■ When adding or subtracting, we round to the fewest places

past the decimal point.

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures?

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures? (a) 13 km 7 min = 1.857 km/min

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures? (a) 13 km 7 min = 1.857 km/min (b) −13 km 7 min = −1.857 km/min

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures? (a) 13 km 7 min = 1.857 km/min (b) −13 km 7 min = −1.857 km/min (c) −70 km 7 min = −10 km/min

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures? (a) 13 km 7 min = 1.857 km/min (b) −13 km 7 min = −1.857 km/min (c) −70 km 7 min = −10 km/min (d) −57 km 7 min = −8 km/min

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures? (a) 13 km 7 min = 1.857 km/min (b) −13 km 7 min = −1.857 km/min (c) −70 km 7 min = −10 km/min (d) −57 km 7 min = −8 km/min (e) 13 km 7 min = 2 km/min

Velocity January 23, 2013 - p. 6/12

Significant Figures Exercise

A car travels from x = −70 km to x = −57 km in 7 minutes. What is the car’s average velocity, in kilometers per minute, recorded to the proper number of significant figures? (a) 13 km 7 min = 1.857 km/min (b) −13 km 7 min = −1.857 km/min (c) −70 km 7 min = −10 km/min (d) −57 km 7 min = −8 km/min (e) 13 km 7 min = 2 km/min

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion.

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr?

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr? (a) 5 cm s × 1 in 2.54 cm × 3600 s 1 h = 7090 in/hr

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr? (a) 5 cm s × 1 in 2.54 cm × 3600 s 1 h = 7090 in/hr (b) 5 cm s × 2.54 cm 1 in × 3600 s 1 h = 45700 in/hr

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr? (a) 5 cm s × 1 in 2.54 cm × 3600 s 1 h = 7090 in/hr (b) 5 cm s × 2.54 cm 1 in × 3600 s 1 h = 45700 in/hr (c) 5 cm s × 1 in 2.54 cm × 60 s 1 h = 118 in/hr

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr? (a) 5 cm s × 1 in 2.54 cm × 3600 s 1 h = 7090 in/hr (b) 5 cm s × 2.54 cm 1 in × 3600 s 1 h = 45700 in/hr (c) 5 cm s × 1 in 2.54 cm × 60 s 1 h = 118 in/hr (d) 5 cm s × 1 in 2.54 cm × 1 h 3600 s = 5.47 × 10−4 in/hr

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr? (a) 5 cm s × 1 in 2.54 cm × 3600 s 1 h = 7090 in/hr (b) 5 cm s × 2.54 cm 1 in × 3600 s 1 h = 45700 in/hr (c) 5 cm s × 1 in 2.54 cm × 60 s 1 h = 118 in/hr (d) 5 cm s × 1 in 2.54 cm × 1 h 3600 s = 5.47 × 10−4 in/hr (e) None of the these

Velocity January 23, 2013 - p. 7/12

Unit Conversion

We use the fact that when multiplying or dividing physical quantities that their units also multiply and divide to simplify unit conversion. Given that 1.00 in = 2.54 cm, which of the following is the correct conversion of 5.00 cm/s into in/hr? (a) 5 cm s × 1 in 2.54 cm × 3600 s 1 h = 7090 in/hr (b) 5 cm s × 2.54 cm 1 in × 3600 s 1 h = 45700 in/hr (c) 5 cm s × 1 in 2.54 cm × 60 s 1 h = 118 in/hr (d) 5 cm s × 1 in 2.54 cm × 1 h 3600 s = 5.47 × 10−4 in/hr (e) None of the these

Velocity January 23, 2013 - p. 8/12

Velocity

Average velocity: vav = ∆x ∆t

Velocity January 23, 2013 - p. 8/12

Velocity

Average velocity: vav = ∆x ∆t Average velocity is a good starting point, but it’s not sufficient for most physics problems, since it only tells you what happens

• n average.

Velocity January 23, 2013 - p. 8/12

Velocity

Average velocity: vav = ∆x ∆t Average velocity is a good starting point, but it’s not sufficient for most physics problems, since it only tells you what happens

• n average.

Instantaneous velocity vx - how fast and the direction of motion for one instant of time.

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion.

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. Position versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. Position versus time Velocity versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. x Position versus time Velocity versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time Velocity versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time vx Velocity versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time t vx Velocity versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time t vx Velocity versus time Horizontal Motion

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time t vx Velocity versus time Horizontal Motion Vertical Motion

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time t vx Velocity versus time Horizontal Motion Vertical Motion t y Position versus time

Velocity January 23, 2013 - p. 9/12

Motion Graphs

Physicists like to make graphs to describe motion. t x Position versus time t vx Velocity versus time Horizontal Motion Vertical Motion t y Position versus time t vy Velocity versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity

b b b b

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2 x1

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2 x1 x2

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2 x1 x2 t2 − t1 = ∆t

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2 x1 x2 t2 − t1 = ∆t x2 − x1 = ∆x

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2 x1 x2 t2 − t1 = ∆t x2 − x1 = ∆x vx = ∆x ∆t

Velocity January 23, 2013 - p. 10/12

Uniform Motion Position Graph

Uniform Motion - Constant velocity Walking to right motion diagram:

b b b b

Equal spacing between dots because with constant velocity the

• bject travels the same distance during equal elapsed times.

t x Position versus time In uniform motion, position is a straight line t1 t2 x1 x2 t2 − t1 = ∆t x2 − x1 = ∆x vx = ∆x ∆t Velocity is the slope of the position versus time graph

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. In math, the slope of line tells you how "steep" a line is.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 In math, the slope of line tells you how "steep" a line is.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1 In Physics, the slope of line is the ratio of the change in two physical quantities.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1 t(s) x(m) In Physics, the slope of line is the ratio of the change in two physical quantities.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1 t(s) x(m) In Physics, the slope of line is the ratio of the change in two physical quantities.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1 t(s) x(m) 1 2 3 15 30 In Physics, the slope of line is the ratio of the change in two physical quantities.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1 t(s) x(m) 1 2 3 15 30 ∆t = 1 s ∆x = 15 m In Physics, the slope of line is the ratio of the change in two physical quantities.

Velocity January 23, 2013 - p. 11/12

Math and Physics Slopes

In Physics, slopes have units and don’t necessarily correspond to the steepness of the line on the drawing. 1 2 3 1 2 run rise In math, the slope of line tells you how "steep" a line is. Slope: m = rise run = 1 1 = 1 t(s) x(m) 1 2 3 15 30 ∆t = 1 s ∆x = 15 m In Physics, the slope of line is the ratio of the change in two physical quantities.

Slope = Velocity: vx = ∆x ∆t = 15 m 1 s = 15 m/s

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point t x (a)

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point t x (a) t x (b)

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point t x (a) t x (b) t x (c)

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point t x (a) t x (b) t x (c) t x (d)

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point t x (a) t x (b) t x (c) t x (d) t x (e)

Velocity January 23, 2013 - p. 12/12

Position Graph Exercise

A man walks some distance to the right with constant speed, immediately turns around and walks back to his starting point with the same speed. Which of the following is the correct position-versus-time graph? Motion Diagram:

b b b b b b b b

Same Point t x (a) t x (b) t x (c) t x (d) t x (e)