When a motorcyle moving with a unifrom speed 11 m/s is at a distance 24 m from a car, the car starts from rest and moves with a uniform acceleration `2 m//s^(2)` away from the motorcyle. If the car begins motion at `t = 0`, time at which the motorcyle will overtake the car is `t = ?`

Options

A. 8 sec
B. 6 sec
C. 3 sec
D. 1.5 sec

Answer

C

Explanation

Let motorcycle meets the car after time t.
For motorcycle: `x = 11 t + 24`
For car: `x = (1)/(2) at^(2)`
`24 + 11 t = (1)/(2) xx 2 xx t^(2)`
`t^(2) - 11 t - 24 = 0`
`t = 3 sec`