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

Answer:

180 m

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;

             $d = ut + \frac{1}{2}at^{2}$

but u = 0

             $d = \frac{1}{2}at^{2}$

             $d = \frac{1}{2}10t^{2}$

             $d = 5t^{2}$               .....(2)

Equating equation (1) and (2)

            30t = 5t²

            $\frac{t^{2}}{t} = \frac{30}{5}$

            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