Question

A motorist with an expired license tag travels at a constant speed of 11.8 m/s down a street, and a policeman on a motorcycle, taking another 4.26 s to finish his donut, gives chase at an acceleration of 2.81 m/s2.

(a) Find the time required to catch the car.

(b) Find the distance the trooper travels while overtaking the motorist.

Answer 1

The policeman has to travel same distance as motorist

time taken to finish the donut = 4.26 sec

distance covered by motorist in this time = 11.8 * 4.26 = 50.268 m

so,

equation for motorist = 50.268 + 11.8 t

equation for policeman = 1.405t²

set them equal

50.268 + 11.8 t = 1.405t²

1.405t² - 11.8 t - 50.268 = 0

t = 11.8 + / - 20.536 / 2.81

t = 11.5 sec

and

distance covered in this time

d = 1/2 * 2.81 * 11.5²

d = 185.8 m