Acar 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?

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;

but u = 0

                            .....(2)

Equating equation (1) and (2)

            30t = 5t²

            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

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