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?

Dec 29, 2016

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 $5 \frac{m}{s}$, the amount of energy (in Joules) that has been added to the system is:

$E = \frac{1}{2} m {V}^{2}$

where V is the speed of the car (in $\frac{m}{s}$) and m is the mass of the car (in kg).

$E = \frac{1}{2} \left(4 k g\right) {\left(5 \frac{m}{s}\right)}^{2}$

$E = 50 J$

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

$P = I E$

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

$P = \left(7 A\right) \left(2 V\right)$

$P = 14 W$

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

$1 W = 1 \frac{J}{s}$

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:

$14 W = \frac{50 J}{t}$

where t is the time of the acceleration in seconds.

Solving for t:

$t = \frac{50 J}{14 W}$

$t \approx 3.57 s$