Question

An electric toy car with a mass of `3 kg` is powered by a motor with a voltage of `9 V` and a current supply of `3 A`. How long will it take for the toy car to accelerate from rest to `5/2 m/s`?

Answer 1

`~~0.35s`

Explanation:

Given

• `m->"Mass of the car"=3kg`
• `V->"The supplied voltage"=9V`
• `I->"Current supply"=3A`

• `u->"Initial velocity of the car"=0`

• `v->"Final velocity of the car"=5/2=2.5m/s`

Let

• `t->"Time taken to gain the final velocity"=?`

Now we know

• `"The Electrical Power supplied"(P)=IxxV`

and

• `"The electrical energy(E) consumed in t s"=Pxxt`

`=>E=VxxIxxt`

• `"The gain in kinetic energy"=1/2m(v^2-u^2)=1/2mv^2`

Considering that the supplied electrical energy goes to increase the KE of the car.

So
`E=1/2mv^2`

`=>VxxIxxt=1/2mv^2`

`:.t=1/2(mv^2)/(VxxI)=1/2(3xx(2.5)^2) /(9xx3)=6.25/18~~0.35s`