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#?

1 Answer
Douglas K.
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 #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#

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