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

The time required to stop a car of mass 2m traveling at speed v is 2 times the time required to stop a car of mass m.

Step-by-step explanation:

To find the time required to stop a car of mass 2m traveling at speed v, we can use the equation F = ma, where F is the braking force, m is the mass, and a is the acceleration. Since the braking force is independent of mass, it will be the same for both cars. Therefore, the acceleration experienced by the car of mass 2m will be half of the acceleration experienced by the car of mass m. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for t:

v = u + at

0 = v - (1/2)at

t = 2v/a

So, the time required to stop a car of mass 2m traveling at speed v is 2 times the time required to stop a car of mass m.

Answer 2

option D

Step-by-step 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' = (F)/(2m)`

from equation (1)

`a' = (a)/(2)`

using equation of motion

v = u + at

0 = v - a t

`t = (v)/(a)`

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

`t'= (v)/(a')`

`t' = 2(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