An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #4 V# and a current supply of #2 A#. How long will it take for the toy car to accelerate from rest to #7/2 m/s#?

Question

An electric toy car with a mass of #4 kg# is powered by a motor with a voltage of #4 V# and a current supply of #2 A#.  How long will it take for the toy car to accelerate from rest to #7/2 m/s#?

Nora Arzate · Accepted Answer

#3.06 "s"#

The product of voltage and current is the power input.

#P = IV#

#= (4 "V") * (2 "A")#

#= 8 "W"#

The vehicle's change in kinetic energy 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"#

The energy divided by the power equals the amount of time required.

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

#= frac{24.5 "J"}{8 "W"}#

#= 3.06 "s"#

Xavier Adame · Answer

undefined To calculate the time it takes for the toy car to accelerate from rest to $ \frac{7}{2} $ m/s, you can use the equation $ t = \frac{m \cdot v}{F} $, where $ t $ is the time, $ m $ is the mass of the car, $ v $ is the final velocity, and $ F $ is the force acting on the car. First, calculate the force using $ F = m \cdot a $, where $ a $ is the acceleration. Then, use $ a = \frac{F}{m} $ to find the acceleration. Finally, use the formula $ v = u + at $, where $ u $ is the initial velocity (0 m/s). Rearrange this equation to solve for $ t $.