# An electric toy car with a mass of 2 kg is powered by a motor with a voltage of 9 V and a current supply of 4 A. How long will it take for the toy car to accelerate from rest to 2/5 m/s?

Feb 26, 2017

Since this is a lot of current from a 9V source, the time required to reach the desired speed is only 4.4 ms (0.0044 s).

#### Explanation:

One real advantage of using energy to solve problems is that we are able to bridge from electrical to mechanical applications with ease. This problem is good example of this.

In terms of the electrical quantities, we look at the power delivered by the electricity.

$P = I \times V$

$P$ is the power, $I$ the current and $V$ the applied voltage.

So, #P = (9 V)(4A) = 36 W.

36 watts means 36 joules of energy supplied per second.

Now, the mechanical stuff:

To accelerate from zero to $\frac{2}{5}$ m/s involves a kinetic energy change of $\frac{1}{2} m {v}_{f}^{2} - \frac{1}{2} m {v}_{i}^{2} = \frac{1}{2} \left(2\right) {\left(\frac{2}{5}\right)}^{2} - 0 = 0.16 J$

Since energy is being supplied at a rate of 36 J/s, the time required is found by:

$P = \frac{E}{t}$ which we write as $t = \frac{E}{P} = \frac{0.16 J}{36 \left(\frac{J}{s}\right)} = 0.0044 s$