Question

An electric toy car with a mass of `4 kg` is powered by a motor with a voltage of `2 V` and a current supply of `7 A`. How long will it take for the toy car to accelerate from rest to `5 m/s`?

Answer 1

Use the Kinetic Energy of the car and the power of the motor to compute the time.

Explanation:

Here is a reference for Power and Energy

When the car reaches the speed of `5m/s`, the amount of energy (in Joules) that has been added to the system is:

`E = 1/2mV^2`

where V is the speed of the car (in `m/s`) and m is the mass of the car (in kg).

`E = 1/2(4 kg)(5m/s)^2`

`E = 50J`

The power (in Watts) being supplied to the motor is:

`P = IE`

where I is the current (in Amperes) and E is the voltage (in Volts)

`P = (7A)(2V)`

`P = 14W`

One of the ways to breakdown the Watt into other units is:

`1 W = 1 J/s`

We are not given an efficiency for the motor, therefore, we must assume that it is 100% efficient. This is not a bad assumption, because it is quite easy to obtain 98% efficiency from an electric motor.

The following equation will give a consistent set of units where 100% of the power supplied to the electric motor went into the kinetic energy of the car:

`14W = (50J)/t`

where t is the time of the acceleration in seconds.

Solving for t:

`t = (50J)/(14W)`

`t ~~ 3.57s`