# Problem: A battery-operated car utilizes a 12.0 V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a 2.00×102 m high hill, and then cause it to travel at a constant 25.0 m/s by exerting a 5.00×102 N force for an hour.

###### FREE Expert Solution

As the car is moving, it also gains height.

Therefore, it has both kinetic and potential energy due to height.

At the top, the car then moves at a constant speed by exerting some force creating energy Fd.

The total energy the car spends is given by:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}{\mathbf{+}}{\mathbf{F}}{\mathbf{d}}}$

At a constant speed, after climbing the hill, the car covers a distance given d = vt

d = (25.0)(1 × 3600) = 90000m

The energy released by the battery is E = qV

85% (367 ratings) ###### Problem Details

A battery-operated car utilizes a 12.0 V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a 2.00×102 m high hill, and then cause it to travel at a constant 25.0 m/s by exerting a 5.00×102 N force for an hour.