A bus starts from rest with a constant acceleration of 5 m s -2. At the same time a car travelling with constant velocity of 50 m s -1 passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed?

Question

A bus starts from rest with a constant acceleration of 5 m s -2. At the same time a car travelling with constant velocity of 50 m s -1 passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed? (A) 25 m s -1 (B) 50 m s -1 (C) 75 m s -1 (D) 100 m s -1

Tardigrade Admin · Accepted Answer

Let the bus overtake the car after time

t

at distance

s

.
Using the relation,

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

For bus,

s = 0 + \frac{1}{2} \times 5 \times t^{2}

For car,

s = 50 t;

∴ \frac{5}{2} t^{2} = 50 t

or

t = 20 s

If

v

is the velocity of the bus after time

t

, then

v = 0 + 5 \times 20 = 100 m s^{- 1}

Q. A bus starts from rest with a constant acceleration of $5 m s^{- 2}$ . At the same time a car travelling with constant velocity of $50 m s^{- 1}$ passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed?

$25 m s^{- 1}$

$50 m s^{- 1}$

$75 m s^{- 1}$

$100 m s^{- 1}$

Q. A bus starts from rest with a constant acceleration of 5ms−2. At the same time a car travelling with constant velocity of 50ms−1 passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed?

25ms−1

50ms−1

75ms−1

100ms−1

Let the bus overtake the car after time t at distance s. Using the relation, s=ut+21​at2 For bus, s=0+21​×5×t2 For car, s=50t; ∴25​t2=50t or t=20s If v is the velocity of the bus after time t, then v=0+5×20=100ms−1

Q. A bus starts from rest with a constant acceleration of $5 m s^{- 2}$ . At the same time a car travelling with constant velocity of $50 m s^{- 1}$ passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed?

$25 m s^{- 1}$

$50 m s^{- 1}$

$75 m s^{- 1}$

$100 m s^{- 1}$