# Problem: A battery-operated car utilizes a 120.0 V source.Find the charge the batteries must be able to move in order to accelerate the 720 kg car from rest to 25 m/s, make it climb a 1.85 x 102 m high hill, and then cause it to travel at a constant 25 m/s by exerting a 5.1 x 102 N force for an hour.

###### FREE Expert Solution

Work done by a battery:

$\overline{){\mathbf{W}}{\mathbf{=}}{\mathbf{q}}{\mathbf{V}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Gravitational potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Work done by constant force:

$\overline{){\mathbf{W}}{\mathbf{=}}{\mathbf{F}}{\mathbf{·}}{\mathbf{d}}}$

The work done on the car is divided into three:

1. Accelerating the car. Work done is equal to the kinetic energy of the car.

2. Climbing a hill. work done is equal to gravitational potential energy.

###### Problem Details

A battery-operated car utilizes a 120.0 V source.

Find the charge the batteries must be able to move in order to accelerate the 720 kg car from rest to 25 m/s, make it climb a 1.85 x 102 m high hill, and then cause it to travel at a constant 25 m/s by exerting a 5.1 x 102 N force for an hour.