What is the option?

Air track car A has mass m and velocity v. Air track car B has mass 2m and velocity 3v. The same constant force F is applied to each car until it stops. Car A is brought to rest in time t. The time required to stop car B is:
(A) 2t (B) 3t (C) 6t (D) 9t and (E)18t

1 Answer
Aug 4, 2018

I get (C)

Explanation:

Car A
It is clear that the force is a retarding force.

Deceleration =F/m

Using the kinematic expression

v=u+at .........(1)

we have

0=v+(-F/m)t
=>t=(vm)/F ......(2)

Car B

Deceleration =F/(2m)

Using (1) we get

0=3v+(-F/(2m))t_B
=>t_B=(3vxx2m)/F
=>t_B=(6vm)/F

Using (2)

=>t_B=6t