Question

A car of mass m, traveling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is independent of mass, what time would be required to stop a car of mass 2m traveling at speed v?
A.½tB. t√C. 2 tD. 2t

Answer 1

Answer:

option D

Explanation:

given,

mass of the car 1 = m

speed of car 1 = v

time taken to stop the car = t

mass of car 2 = m' = 2 m

speed of the car 2 = v

time taken by the car to stop = t' = ?

now,

we know,

F = m a....(1)

and force by the second car

F = m' a'

F = 2 m a'

$a' = \dfrac{F}{2m}$

from equation (1)

$a' = \dfrac{a}{2}$

using equation of motion

v = u + at

0 = v - a t

$t = \dfrac{v}{a}$

again using equation of motion for the calculation of the time taken by the second car.

$t'= \dfrac{v}{a'}$

$t' = 2\dfrac{v}{a}$

t' = 2 t

hence, the time taken by the second car is twice the time taken by the first car to stop.

The correct answer is option D