1. A particle moves along the `x` axis according to the equation `x=2.00+3.00t -1.00t^2`, where `x` is in meters and `t` is in seconds. At `t = 3.00 s`, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.

2. A velocity–time graph for an object moving along the x axis is shown in Figure P2.13. (a) Plot a graph of the acceleration versus time. Determine the average acceleration of the object (b) in the time interval `t=5.00s` to `t=15.0s` and (c) in the time interval `t = 0` to `t = 20.0 s`.

3. A `50.0 g` Super Ball traveling at `25.0 m//s` bounces off a brick wall and rebounds at `22.0 m//s`. A high-speed camera records this event. If the ball is in contact with the wall for `3.50 ms`, what is the magnitude of the average acceleration of the ball during this time interval?

4. An object moves with constant acceleration `4.00 m//s^2` and over a time interval reaches a final velocity of `12.0 m//s`. (a) If its initial velocity is `6.00 m//s`, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its initial velocity is `-6.00 m//s`, what is its displacement during the time interval? (d) What is the total distance it travels during the interval in part (c) ?

5. A jet comes in for a landing on solid ground with a speed of `100 m//s`, and its acceleration can have a maximum magnitude of `5.00 m//s^2` as it comes to rest. (a) From the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest? (b) Can this jet land at a small tropical island airport where the runway is `0.800 km` long? (c) Explain your answer.

6. At time `t = 0`, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance `h` above. The second student catches the keys at time `t`. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

7. A ball is thrown directly downward with an initial speed of `8.00 m//s` from a height of `30.0 m`. After what time interval does it strike the ground?