Question

A motor does 20. joules of work on a block, accelerating the block vertically upward. Neglecting friction, if the gravitational potential energy of the block increases by 15 joules, its kinetic energy does what?

Answer 1

The motor does 20 J of work on the block, it means that the total mechanical energy of the block has increased by 20 J. But the increase in total mechanical energy is equal to the sum of the increases in potential energy and kinetic energy:
$\Delta E = \Delta U + \Delta K$
So, if the gravitational potential energy has increased by 15 J, the kinetic energy has increased by
$\Delta K = \Delta E - \Delta U = 20 J - 15 J= 5 J$