# 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 1 m/s?

Oct 5, 2017

This is a problem for the use of the principle of conservation of energy. The car's kinetic energy when its speed is up to $1 \frac{m}{s}$ is
$K E = \frac{1}{2} \cdot 2 k g \cdot {\left(1 \frac{m}{s}\right)}^{2} = 1 k g \cdot {m}^{2} / {s}^{2} = 1 J$

So, how long does it take that motor to deliver 1 J of energy? The power being consumed by the motor is given by
$P = E \cdot I = 4 V \cdot 2 A = 8 W$

$P o w e r \cdot t i m e = \text{energy}$, therefore $P o w e r = \text{energy"/"time}$.
The unit Watt is equivalent to the combination of units $\frac{\text{Joule}}{\sec}$. Therefore the motor is consuming power from the voltage supply at the rate of $8 \frac{J}{s}$.

So
$8 \frac{J}{s} \cdot t = 1 J$
$t = \frac{1 \cancel{J}}{8 \frac{\cancel{J}}{s}} = 0.125 s$

Note that we are ignoring the fact that the motor will warm up which wastes some of the power. Ignoring such losses simplify the problem. So it will get more complicated in the future - but, don't panic.

I hope this helps,
Steve