# An electric toy car with a mass of 5 kg is powered by a motor with a voltage of 1 V and a current supply of 6 A. How long will it take for the toy car to accelerate from rest to 4/5 m/s?

Jan 11, 2017

It will take only 0.27 s to reach this speed.

#### Explanation:

This problem will be solved using energy considerations, demonstrating the ease with which energy connects different situations - electrical and mechanical.

Given the current and voltage supplied to the motor, we can calculate the power output:

$P = I \times V = 6$ watts

This means that work is being done on the car at a rate of 6 joules per second.

For the rest of the problem, we will continue to work in energy terms.

The kinetic energy of the car, must change from zero to

$K = \frac{1}{2} m {v}^{2} = \frac{1}{2} \left(5\right) {\left(\frac{4}{5}\right)}^{2} = 1.6 J$

Since work is being done at 6 J/s, the time required will be:

$\frac{1.6 J}{6 \frac{J}{s}} = 0.27 s$