1. Lecture 5: Motion in One Dimension With Changing Velocity
Physics 31
Lecture 5:
Motion in One Dimension
With Changing Velocity

2. v(t) from x(t)

3. v(t) is slope of x(t)

4. x(t) from v(t)
v(t) t
tend
What does x(t) look like?

5. v(t) = constant=10m/s 1. How far would the object travel in one second
v(t) = constant=10m/s 1. How far would the object travel in one second? 2. How far in two seconds?

6. Slope is v = constant
x(t) t

7. Acceleration Acceleration is: The rate of change of velocity
The slope of a velocity- versus-time graph
Slide 2-20

8. Checking Understanding
These four motion diagrams show the motion of a particle along the x-axis. Rank these motion diagrams by the magnitude of the acceleration. There may be ties.
Answer: A, B, C, D are the same magnitude acceleration.
Slide 2-21

9. Checking Understanding
These four motion diagrams show the motion of a particle along the x-axis. Which motion diagrams correspond to a positive acceleration? Which motion diagrams correspond to a negative acceleration?
Answer: Positive: A, C; negative: B, D
Slide 2-22

10. Checking Understanding
These six motion diagrams show the motion of a particle along the x-axis. Rank the accelerations corresponding to these motion diagrams, from most positive to most negative. There may be ties.
Answer: A & D, E & F, B & C
Slide 2-23

11. Acceleration—Rate of Change of Velocity

12. v(t) from a(t)

13. x(t) from v(t) x(t) is the area under the v(t) vs t curve
For constant a

14. In general, for constant acceleration

15. Quiz, question 1
Here is a motion diagram of a car moving along a straight stretch of road:
Which of the following velocity-versus-time graphs matches this motion diagram?
Answer: C A. B. C. D.
Slide 2-13

16. Question 2
A graph of position versus time for a basketball player moving down the court appears like so:
Which of the following velocity graphs matches the above position graph?
Answer: C A. B. C. D.
Slide 2-15

17. Question 3
A car is moving with a constant velocity in the positive x-direction along a straight road. The magnitude of the velocity is v=12 m/s. Ten seconds later, it crashes into a wall and stops very suddenly.
A) sketch v(t) versus t for the first 15 seconds.
B) sketch x(t) versus t for the first 15 seconds.

18. Homework due Monday Reading 2: 3-4 Motion with constant acceleration
Problems: 2: CQ1, CQ6, MC18, 1, 3, 5, 8, 12