An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #15 V# and a current supply of #15 A#. How long will it take for the toy car to accelerate from rest to #5 m/s#?

Question

1064 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-19T04:06:00

#0.222 "s"#

The power input is the product of the voltage and the current.

#P = IV#

#= (15 "V") * (15 "A")#

#= 225 "W"#

The change in kinetic energy for the car is

#Delta "KE" = 1/2 m (v^2 - v_0^2)#

#= 1/2 (4 "kg") ((5 "m/s")^2 - (0 "m/s")^2)#

#= 50 "J"#

Thus, the time needed is the energy divided by the power.

#t = frac{Delta "KE"}{P}#

#= frac{50 "J"}{225 "W"}#

#= 0.222 "s"#

Btw there should be some kind of error. A toy car wouldn't have that kind of batteries.