An electric toy car with a mass of $5 k g$ $5 kg$ is powered by a motor with a voltage of $3 V$ $3 V$ and a current supply of $8 A$ $8 A$ . How long will it take for the toy car to accelerate from rest to $\frac{3}{2} \frac{m}{s}$ $3/2 m/s$ ?

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Answer 1 · 2016-03-18T04:58:48

$0.234 s$ $0.234 "s"$

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

$P = I V$ $P = IV$

$= (3 V) \cdot (8 A)$ $= (3 "V") * (8 "A")$

$= 24 W$ $= 24 "W"$

The change in kinetic energy for the car is

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

$= 1/2 (5 "kg") ((3/2 "m/s")^2 - (0 "m/s")^2)$

$= 5.625 "J"$

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

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

$= frac{5.625 "J"}{24 "W"}$

$= 0.234 "s"$

An electric toy car with a mass of 5 kg5kg5 kg is powered by a motor with a voltage of 3 V3V3 V and a current supply of 8 A8A8 A. How long will it take for the toy car to accelerate from rest to 3/2 m/s32ms3/2 m/s?