Answer:
The correct option is: B that is 1/2 K
Explanation:
Given:
Two carts of different masses, same force were applied for same duration of time.
Mass of the lighter cart = 
Mass of the heavier cart = 
We have to find the relationship between their kinetic energy:
Let the KE of cart having mass m be "K".
and KE of cart having mass m be "K1".
As it is given regarding Force and time so we have to bring in picture the concept of momentum Δp and find a relation with KE.
Numerical analysis.
⇒
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Now,
Kinetic energies and their ratios in terms of momentum or impulse.
KE (K) of mass m.
⇒
...equation (i)
KE (K1) of mass 2m.
⇒ 
⇒
...equation (ii)
Lets divide K1 and K to find the relationship between the two carts's KE.
⇒ 
⇒ 
⇒ 
⇒ 
⇒
⇒ 
The kinetic energy of the heavy cart after the push compared to the kinetic energy of the light cart is 1/2 K.
Answer:
(a) -472.305 J
(b) 1 m
Explanation:
(a)
Change in mechanical energy equals change in kinetic energy
Kinetic energy is given by
Initial kinetic energy is 
Since he finally comes to rest, final kinetic energy is zero because the final velocity is zero
Change in kinetic energy is given by final kinetic energy- initial kinetic energy hence
0-472.305 J=-472.305 J
(b)
From fundamental kinematic equation

Where v and u are final and initial velocities respectively, a is acceleration, s is distance
Making s the subject we obtain
but a=\mu g hence

change in position of an object we use the
symbol ∆×\ delta×∆×for displacement, where ∆. means
"change" ∆ vector quantity with units of distances start
text ,d,I,s,t,a,n,c,e , end text.