Answer the questions with completed solutions.

1. A police car chases a speeder who is travelling at 125 km/h. The maximum speed of the police car is 190 km/h. The police car travels from rest with a constant acceleration of 8.00 km/hs until its speed reaches 190 km/h. It then moves at constant speed. (a) When does the police car catch the speeder if it starts just as the speeder passes? (b) How far has each car travelled? (c) Sketch x(t) for each car.

2. A proton moves along thexaxis according to the equationx= 50t+ 10t2, wherexis in meters andtis in seconds. Calculate (a) the average velocity of the proton during the first 3.0 s of its motion, (b) the instantaneous velocity of the proton att= 3.0 s, and (c) the instantaneous acceleration of the proton att= 3.0 s. (d) Graphxversustand indicate how the answer to (a) can be obtained from the plot. (e) Indicate the answer to (b) on the graph. (f) Plotvversustand indicate on it the answer to (c).

Answers

1. a) 34.7 s b) 1.21 km.
2. a) 80 m/s b) 110 m/s c) 20 m/s2