Physics--K.E & momentum?

Question

25% of momentum increase of an object cause how much % increase in K.E?? please evaluate it

Answer 1

there will be a 1.5625 times or a 56.25 % increase in kinetic energy

Answer 2

Let m = mass,

v1 = initial velocity

v2 = velocity when momentum has increased

Momentum = mass * velocity

mv2 = mv1 + 25% of mv1

v2 = v1 + 25% of v1

Or, v2 = 1.25 v1

Initial KE = K1 = 1/2 mv1^2

Final KE = K2 = 1/2 mv2^2

Increase in KE = 1/2 m(v2^2 - v1^2) = 1/2 m(1.25^2 * v1^2 - v1^2)

= 1/2 mv1^2 (1.25^2 - 1)

% increase in KE = 1/2 mv1^2 (1.25^2 - 1)/(1/2 mv1^2)  * 100%

= (1.25^2 - 1) * 100 % = 56.25 %

Answer 3

It will be around 56%...not very sure