# An electric toy car with a mass of 5 kg is powered by a motor with a voltage of 4 V and a current supply of 5 A. How long will it take for the toy car to accelerate from rest to 3/2 m/s?

Oct 6, 2017

$\text{time" = 1.125" s}$

#### Explanation:

$\text{Power"_"in} =$ the power supplied by the battery

$\text{Power"_"in" = "Current" xx "Voltage}$

"Power"_"in" = (4" V")(5" A")

$\text{Power"_"in" = 20" W}$

"Power"_"out" = ("Kinetic Energy")/("time")

"Power"_"out" = (1/2 "Mass"("Speed")^2)/("time")

"Power"_"out" = (1/2(5" kg")(3" m/s")^2)/("time")

"Power"_"out" = (22.5" J")/("time")

We are not given an efficiency of the system, therefore, we must assume that:

$P o w e {r}_{\text{in" = Power_"out}}$

20" W"= (22.5" J")/("time")

"time" = (22.5" J")/(20" W")

$\text{time" = 1.125" s}$