Question

If the linear momentum is increased by 50% then how K.E will be increased by 125%?

Answer 1

new momentum = m' v' = 1.50 m v

1)  KE is to be increased by 25% to 125% of its previous value:
         given, new KE = 1/2  m' v' * v'  = 1.25 * 1/2 m v * v
                     => 1/2 * 1.50  m v  * v'  = 1/2 * 1.25 * m v * v
                     => 1.50 v' = 1.25 v
                     =>  v'  =  5/6 * v              => reduce speed to 5/6th of its value.

2)  KE is to be increased by 125% to  become 225% of its value.
         given,  new KE = 1/2 m' v' v' = 2.25 * 1/2 m v * v
                =>  1.50  v' = 2.25 v
                       v' =  1.50 v             increase speed by 50% to become 3/2 times.