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?

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

Tardigrade Admin · Accepted Answer

Let the bus overtakes the car after time

t

and at distance

d

.
Bus (accelerated motion)

u = 0

a = 8 m s^{- 2}

S = u t + \frac{1}{2} a t^{2}

= \frac{1}{2} \times 8 \times t^{2}

... (i)
Car (uniform motion)

v = 16 m s^{- 1}

S = v t

= 16 t

... (ii)
Solving Eqs. (i) and (ii), we get

t = 4 s, d = 64 m

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

t = 4 s, d = 64 m

t = 5s , d = 72 m

t = 8 s, d = 58 m

None of the above

Let the bus overtakes the car after time t and at distance d. Bus (accelerated motion) u=0 a=8ms−2 S=ut+21​at2 =21​×8×t2 ... (i) Car (uniform motion) v=16ms−1 S=vt =16t ... (ii) Solving Eqs. (i) and (ii), we get t=4s,d=64m

Q. A bus starts from rest and moves with constant acceleration $8 m s^{- 2}$ . 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?