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#?

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Answer 1 · 2017-10-06T17:44:40

#"time" = 1.125" s"#

#"Power"_"in" =# the power supplied by the battery

#"Power"_"in" = "Current" xx "Voltage"#

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

#"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:

#Power_"in" = Power_"out"#

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

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

#"time" = 1.125" s"#