An electric toy car with a mass of 2kg is powered by a motor with a voltage of 4V and a current supply of 8A. How fast can the toy car accelerate from rest to 3ms?

1 Answer
JMicheli
Jun 28, 2016

The car will take 932 seconds or about 3.5 seconds.

Explanation:

Voltage and current relate to power by the equation P=IV.

Power in turn, relates to work by the equation P=Wt.

Kinetic energy is simply a measure of work and has the form W=KE=12mv2.

So in order to solve this, we first determine the power output of the motor. This is P=4⋅8=32.

Using this result and the second equation, we can rearrange terms to show that Pt=32t=W so now we only have to figure out how much W is and solve for t.

Using the third equation and plugging in the given values, we can see that W=KE=12⋅2⋅32=9.

The rest is trivial algebra. Using Pt=W=KE we get 32t=9 which means t=932.

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