An electric toy car with a mass of #6 kg# is powered by a motor with a voltage of #7 V# and a current supply of #6 A#. How long will it take for the toy car to accelerate from rest to #4 m/s#?
We can suggest two solutions.
Energy conservation approach leads to following solution.
The beginning kinetic energy of a toy car is zero. Ending energy is
This is exactly the amount of work (
Power of the electric motor, that is its voltage times current (
Different approach is related to analyzing the force and distance.
Assume, the time to accelerate from rest (
That means, acceleration equals to
The distance covered by a toy car equals to
The force of the electric motor that accelerates a toy car equals to its mass times acceleration (Second Newton's Law)
The work performed by a motor equals to force times distance:
The power of the electric motor
The work electric motor performs during the time