An electric toy car with a mass of $4 k g$ $4 kg$ is powered by a motor with a voltage of $8 V$ $8 V$ and a current supply of $15 A$ $15 A$ . How long will it take for the toy car to accelerate from rest to $7 \frac{m}{s}$ $7 m/s$ ?

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Answer 1 · 2016-03-19T04:08:17

$0.817 s$ $0.817 "s"$

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

$P = I V$ $P = IV$

$= (8 V) \cdot (15 A)$ $= (8 "V") * (15 "A")$

$= 120 W$ $= 120 "W"$

The change in kinetic energy for the car is

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

$= 1/2 (4 "kg") ((7 "m/s")^2 - (0 "m/s")^2)$

$= 98 "J"$

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

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

$= frac{98 "J"}{120 "W"}$

$= 0.817 "s"$

An electric toy car with a mass of 4 kg4kg4 kg is powered by a motor with a voltage of 8 V8V8 V and a current supply of 15 A15A15 A. How long will it take for the toy car to accelerate from rest to 7 m/s7ms7 m/s?