Question

A bus starts from rest and moves with constant acceleration $8 \,ms ^{-2}$. At the same time, a car travelling with a constant velocity $16\, m / s$ overtakes and passes the bus. After how much time and at what distance, the bus overtakes the car?

• A. t = 4 s, d = 64 m
• B. t = 5s , d = 72 m
• C. t = 8 s, d = 58 m
• D. None of the above

Answer 1

Answer: (A)

Let the bus overtakes the car after time $t$ and at distance $d$.
Bus (accelerated motion) $u=0$
$a =8 \,ms ^{-2} $
$S =u t+\frac{1}{2} a t^{2} $
$=\frac{1}{2} \times 8 \times t^{2}$ ... (i)
Car (uniform motion) $v=16 \,ms ^{-1}$
$S =v t $
$=16 t$ ... (ii)
Solving Eqs. (i) and (ii), we get
$t=4 \,s , d=64 \,m$