An electric toy car with a mass of 6 kg is powered by a motor with a voltage of 4 V and a current supply of 7 A. How long will it take for the toy car to accelerate from rest to 8/3 m/s?

Jul 6, 2016

$t = \frac{16}{21} s$

Explanation:

Since power given by the battery is $P = V I$ and energy is power times total time (depends on how the power equation is), so energy given by battery to car so as to move, if heat is not given is
$W = V I t$

Now, we have to consider it's kinetic energy since that's what the question is about.
So, Kinetic energy equation is $E = \frac{1}{2} m {v}^{2}$

Since all the work done by the battery is considered to be converted to kinetic energy,
$V I t = \frac{1}{2} m {v}^{2}$
We have $V = 4$, $I = 7$, $m = 6$, $v = \frac{8}{3}$. We need to find $t$.
So substitute.

$4 \cdot 7 \cdot t = \frac{1}{2} \cdot 6 \cdot {8}^{2} / {3}^{2} \setminus \implies {\cancel{4}}^{1} \cdot 7 \cdot t = {\cancel{3}}^{1} \cdot {\cancel{64}}^{16} / {\cancel{9}}^{3}$

Rearranging gives us the answer as I have given above.
You can simplify it further yourself.