Question

A car starts with acceleration $2\,m s^{-2}$. A scooterist starts towards the car with a velocity of $20\,ms^{-1}$. If the scooterist was $96\,m$ behind the car at the start, the time in which he overtakes the car is

• A. 8 s
• B. 6 s
• C. 2 s
• D. cannot overtake.

Answer 1

Answer: (A)

8 s

Answer 2

Let $t$ be the required time.
Distance covered by car, S = $\frac{1}{2} \times 2 \times t^2 = t^2$
Distance covered by scooter = 96 + S = 20 t
$\therefore$ $96 + t^2 =20 \, t$ i.e. $t^2 - 20 \, t +96$ = 0
Solving $t$ = 8 s.