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

Sep 6, 2016

It will take $3 s$ to accelerate the car.

#### Explanation:

To accelerate the car to $3 \frac{m}{s}$ engine has to do work equal to the car's end kinetic energy:

$W = {E}_{k} = \frac{m {v}^{2}}{2} = \frac{4 \cdot {3}^{2}}{2} = 2 \cdot 9 = 18 \left[J\right]$

Now to find the time we have to calculate the engine's power:

$P = U \cdot I = 3 \cdot 8 = 24 \left[W\right]$

Finally to calculate the time we have to divide the work/energy by the power:

$t = \frac{W}{P} = \frac{18}{24} = \frac{2}{3} \left[s\right]$