A 5kg object moves to the right with a speed of 2m/s. It collides in a perfectly elastic collision with a 2 kg object moving to the left at 5m/s.What is the total kinetic energy after the collision?

In elastic collisions KE is conserved so KE_i =KE_f
KE_f=1/2(5)(2)^2+ 1/2(2)(5)^2
=10+25
=35 J
Is this correct?

The toal Ke is the same as it started with, that is the definition of an elastaic equation.

Yes, you have it.

Your calculation is not correct. In an elastic collision, both momentum and kinetic energy are conserved.

To find the total kinetic energy after the collision, we need to calculate the initial and final kinetic energies separately, and then compare them.

1. Calculate the initial kinetic energy:
The initial kinetic energy of the 5 kg object is given by KE1_i = 1/2 * mass1 * velocity1^2:
KE1_i = 1/2 * 5 kg * (2 m/s)^2
KE1_i = 1/2 * 5 kg * 4 m^2/s^2
KE1_i = 10 J

The initial kinetic energy of the 2 kg object is given by KE2_i = 1/2 * mass2 * velocity2^2:
KE2_i = 1/2 * 2 kg * (5 m/s)^2
KE2_i = 1/2 * 2 kg * 25 m^2/s^2
KE2_i = 25 J

2. Calculate the final kinetic energy:
Since this is a perfectly elastic collision, both momentum and kinetic energy are conserved. This means that the total initial kinetic energy before the collision is the same as the total final kinetic energy after the collision. Therefore, we can add the initial kinetic energies together to find the final total kinetic energy:
KE_total_f = KE1_i + KE2_i
KE_total_f = 10 J + 25 J
KE_total_f = 35 J

So, the total kinetic energy after the collision is 35 J.

Therefore, your calculation is correct.