Question

a vechicle moving with velocity of 2m/s can be stopped over a distance of 2m keeping retarding force constant if kinetic energy is doubled what is the distance
covered before it comes to rest

Answer 1

According to work energy theorem the change in kinetic energy of a body is equal to the work done by the kinetic energy on the body.
 
            But work done is directly proportional to the displacement if a constant force is acted on the body.
 
So we can conclude that the change in kinetic energy of a body is directly proportional to the displacement if a constant force is acted on the body.
 
As the kinetic energy in the given problem is doubled the displacement of the body also doubles.
     

     So it travells double of 2m = 4m
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