a 5kg rock is dropped from a height of 92m. What is the kinetic energy when the rock is 40m from the ground?

I know that the formula is kinetic energy=1/2mv(squared)

but I don't have the time so how would I find the speed, v?

I don't have the time either, you will have to do it yourself in time for your homework assignment tomorrow.

You can do this in 2 ways, either realise that the loss in potential energy is identical to the gain in kinetic energy, or you can work out the end speed using a SUVAT equation and use the KE equation you have there.

I would say the potential energy way is easier.

Either way, you're going to need to put the work in.

Potential energy at height h = mgh

( m = mass, g = force of gravity)

Kinetic energy at height 92 = 0

Hence loss of potential energy in falling = mg (92 - 40) = 52 mg

Hence Kinetic energy = 52 mg

1/2 mv^2 = 52mg

v^2 = 104g

Substitute value g to get the answer!