An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #3 V# and a current supply of #8 A#. How long will it take for the toy car to accelerate from rest to #7/2 m/s#?
1 Answer
Mar 20, 2016
The power input is the product of the voltage and the current.
#P = IV#
#= (3 "V") * (8 "A")#
#= 24 "W"#
The change in kinetic energy for the car is
#Delta "KE" = 1/2 m (v^2 - v_0^2)#
#= 1/2 (4 "kg") ((7/2 "m/s")^2 - (0 "m/s")^2)#
#= 24.5 "J"#
Thus, the time needed is the energy divided by the power.
#t = frac{Delta "KE"}{P}#
#= frac{24.5 "J"}{24 "W"}#
#= 1.02 "s"#
