How does the work done affect the kinetic energy of two carts with different velocities?

Relationship Between Work Done and Kinetic Energy

Work Done on the Cart Going Faster: When one cart is pushed until it is going two times faster than the other cart, the cart going faster has twice the final velocity of the other cart. However, since both carts have the same mass, the work done on both carts will be the same. This is because the work done is determined by the force applied and the distance over which the force is applied, and in this case, the force and distance are the same for both carts.

Final Kinetic Energy: The kinetic energy of an object is related to its velocity. The kinetic energy of an object is given by the equation:
Kinetic energy = 1/2 * mass * velocity²
Since the cart going faster has twice the final velocity of the other cart, its kinetic energy will be four times greater. This means that the cart going faster will have four times more kinetic energy than the other cart.

In summary, the work done on both carts will be the same, but the cart going faster will have four times more kinetic energy than the other cart.