Question

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`?

Answer 1

The car will take `9/32` seconds or about 3.5 seconds.

Explanation:

Voltage and current relate to power by the equation `P = IV`.

Power in turn, relates to work by the equation `P = W/t`.

Kinetic energy is simply a measure of work and has the form `W = KE = 1/2mv^2`.

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

Using this result and the second equation, we can rearrange terms to show that `Pt = 32t = 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 = KE = 1/2*2*3^2 = 9`.

The rest is trivial algebra. Using `Pt = W = KE` we get `32t = 9` which means `t = 9/32`.