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#?
Here is a reference for Power and Energy
When the car reaches the speed of
where V is the speed of the car (in
The power (in Watts) being supplied to the motor is:
where I is the current (in Amperes) and E is the voltage (in Volts)
One of the ways to breakdown the Watt into other units is:
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:
where t is the time of the acceleration in seconds.
Solving for t: