# 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 2 A. How long will it take for the toy car to accelerate from rest to 3 m/s?

May 15, 2017

I tried this:

#### Explanation:

We can say that the power of the motor will be:

$P = V I = 4 \cdot 2 = 8 W$

I would then use the theorem of Work $W$ and Kinetic Energy $K$ to write:

$W = \Delta K$

$W = \frac{1}{2} m {v}_{f}^{2} - \frac{1}{2} m {v}_{1}^{2}$

dividing both sides by the time we get:

$\frac{1}{t} W = \frac{1}{t} \left(\frac{1}{2} m {v}_{f}^{2} - \frac{1}{2} m {v}_{1}^{2}\right)$

$P = \frac{1}{t} \left(\frac{1}{2} m {v}_{f}^{2} \cancel{- \frac{1}{2} m {v}_{1}^{2}}\right)$

because the toy car stars from rest (${v}_{i} = 0$).

so we get:

$8 = \frac{1}{t} \cdot \frac{1}{2} \cdot 2 \cdot {3}^{2}$

rerranging:

$t = \frac{9}{8} = 1.125 s$