1. Motion in a Straight Line

2. Velocity Velocity - Rate of change of position. Average velocity
Instantaneous velocity

3. How fast?
An object moves by the function x(t) = k·t2. What is the speed at t = 2 s? (k = 1m/s2)
At t = 0 s, x = 0 m
4.0
At t = 2.0 s, x = 4.0 m
3.0
Position (m)
2.0
1.0
0.5
1.0
1.5
2.0
Time (s)

4. How fast? (cont.)
An object moves by the function x(t) = k·t2. What is the speed at t = 2 s? (k = 1m/s2)
At t = 2.0 s, v = 4.0 m/s
4.0
3.0
Position (m)
2.0
1.0
0.5
1.0
1.5
2.0
Time (s)

5. Acceleration Acceleration - Rate of change of velocity.
Average acceleration
Instantaneous acceleration

6. Position, Velocity, & Acceleration
2.0
Position vs. Time
1.0
Position (m)
-1.0
-2.0
1.0
2.0
3.0
4.0
5.0
6.0
Time (s)
Locate: Zero displacement, zero velocity, & zero acceleration

7. Kinematic Equation Assumptions Velocity w.r.t. time Average velocity
Constant acceleration
Initial time is 0s
Velocity w.r.t. time
Average velocity
Position w.r.t. time
Velocity w.r.t. position
Note: Use the definitions of velocity and acceleration.

8. Rolling Ball
A ball starts at the top of an 8.00 m long ramp with zero initial velocity. It accelerates at a constant rate of 2.00 m/s2.
How long does it take for the ball to reach the bottom of the ramp?
What is the velocity at the bottom of the ramp?

9. Earth’s Gravity
Near the earth’s surface the acceleration of gravity for an object in free fall is 9.80 m/s2 downward.
Ex. A ball is dropped from a roof at a height of 30.0m. How long does it take to hit the ground?

10. Thrown Ball
A ball is thrown over the edge of a cliff with an upward velocity of 8.00 m/s. The cliff is 12.0 m high. How long after the fall is thrown will it ____.
Reach max height?
Hit the bottom of the cliff? v0

11. Mass on a Spring
The function describing the acceleration of a mass on a spring is
What is the function of velocity if the initial velocity is -5.0 m/s?

12. Stopping a Car
A car traveling at 45 mph collides with a tree. The front of the car crumples 1.0 m before it comes to a halt. What is the average acceleration of the car during the collision? v0