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;
       [tex]d = ut + \frac{1}{2}at^{2}[/tex]
but u = 0
       [tex]d = \frac{1}{2}at^{2}[/tex]
       [tex]d = \frac{1}{2}10t^{2}[/tex]
       [tex]d = 5t^{2}[/tex]        .....(2)
Equating equation (1) and (2)
      30t = 5t²
      [tex]\frac{t^{2}}{t} = \frac{30}{5}[/tex]
      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
