Question

A car travels on a long, straight highway at a constant speed of 30 m/s when it passes a stationary police motorcycle. As the car passes the motorcycle, the motorcycle accelerates at a constant rate of 10 m/s2 to try to catch up to the car. How far will the motorcycle travel before it catches up to the car?

Answer 1

180 m

Step-by-step explanation:

Given:

Uniform speed of the car, U = 30 m/s

Uniform acceleration of the motorcycle = 10 m/s²

For the motorcycle to catch up with the car, the distance traveled must be the same.

For the car;

Distance = Speed × Time

⇒ d = u × t

d = 30 × t

d = 30t ......(1)

For the motorcycle;

The stationary police motorcycle has initial speed, u = 0

From equation of motion;

`d = ut + (1)/(2)at^(2)`

but u = 0

`d = (1)/(2)at^(2)`

`d = (1)/(2)10t^(2)`

`d = 5t^(2)` .....(2)

Equating equation (1) and (2)

30t = 5t²

`(t^(2))/(t) = (30)/(5)`

t = 6 seconds

Substituting t = 6 s into equation (2)

d = 5(6)²

d = 5 × 36

d = 180 m

The motorcycle must travel 180 m before it catches up to the car