# An electric toy car with a mass of 1 kg is powered by a motor with a voltage of 12 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?

Aug 18, 2017

$t \approx 0.0017 \text{s}$

#### Explanation:

Power can be expressed in terms of current and voltage as:

$\textcolor{b l u e}{P = V I}$

• The units of power are watts, where one watt is equivalent to one joule (of energy) per second. We can use this idea along with the concept of kinetic energy to determine the time required to accelerate the toy car to the given velocity.

$\textcolor{b l u e}{K = \frac{1}{2} m {v}^{2}}$

$\implies$where $m$ is the object's mass and $v$ is its velocity.

We have the following information:

• $\mapsto m = 1 \text{kg}$
• $\mapsto V = 12 \text{V}$
• $\mapsto I = 4 \text{A}$
• $\mapsto v = \frac{2}{5} \text{m"//"s}$

We can calculate power:

$P = \left(12 \text{V")(4} A\right)$

$\textcolor{b l u e}{P = 48 \text{ Joules"//"second}}$

Now kinetic energy:

$K = \frac{1}{2} {\left(1 \text{kg")(2/5"m"//"s}\right)}^{2}$

$\textcolor{b l u e}{K = \frac{2}{25} \text{J}}$

So, we have:

2/25cancel("Joules")xx(1"second")/(48cancel(" Joules"))

$\implies 1 / 600 \text{ seconds}$

$\implies \textcolor{b l u e}{\approx 0.0017 \text{ s}}$

Or, in scientific notation, $\approx 1.7 \times {10}^{3} \text{ s}$