# An electric toy car with a mass of 2 kg is powered by a motor with a voltage of 4 V and a current supply of 8 A. How fast can the toy car accelerate from rest to 3 m/s?

##### 1 Answer
Jun 28, 2016

The car will take $\frac{9}{32}$ seconds or about 3.5 seconds.

#### Explanation:

Voltage and current relate to power by the equation $P = I V$.

Power in turn, relates to work by the equation $P = \frac{W}{t}$.

Kinetic energy is simply a measure of work and has the form $W = K E = \frac{1}{2} m {v}^{2}$.

So in order to solve this, we first determine the power output of the motor. This is $P = 4 \cdot 8 = 32$.

Using this result and the second equation, we can rearrange terms to show that $P t = 32 t = W$ so now we only have to figure out how much $W$ is and solve for $t$.

Using the third equation and plugging in the given values, we can see that $W = K E = \frac{1}{2} \cdot 2 \cdot {3}^{2} = 9$.

The rest is trivial algebra. Using $P t = W = K E$ we get $32 t = 9$ which means $t = \frac{9}{32}$.