An electric toy car with a mass of $2 k g$ $2 kg$ is powered by a motor with a voltage of $12 V$ $12 V$ and a current supply of $4 A$ $4 A$ . How long will it take for the toy car to accelerate from rest to $\frac{2}{5} \frac{m}{s}$ $2/5 m/s$ ?

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Answer 1 · 2016-03-19T04:14:46

$0.00195 s$ $0.00195 "s"$

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

$P = I V$ $P = IV$

$= (12 V) \cdot (4 A)$ $= (12 "V") * (4 "A")$

$= 48 W$ $= 48 "W"$

The change in kinetic energy for the car is

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

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

$= 0.16 "J"$

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

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

$= frac{0.16 "J"}{48 "W"}$

$= 0.00195 "s"$

An electric toy car with a mass of 2 kg2kg2 kg is powered by a motor with a voltage of 12 V12V12 V and a current supply of 4 A4A4 A. How long will it take for the toy car to accelerate from rest to 2/5 m/s25ms2/5 m/s?