An electric toy car with a mass of $3 k g$ $3 kg$ is powered by a motor with a voltage of $9 V$ $9 V$ and a current supply of $8 A$ $8 A$ . How long will it take for the toy car to accelerate from rest to $\frac{8}{3} \frac{m}{s}$ $8/3 m/s$ ?

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Answer 1 · 2016-03-18T04:54:13

$0.148 s$ $0.148 "s"$

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

$P = I V$ $P = IV$

$= (9 V) \cdot (8 A)$ $= (9 "V") * (8 "A")$

$= 72 W$ $= 72 "W"$

The change in kinetic energy for the car is

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

$= 1/2 (3 "kg") ((8/3 "m/s")^2 - (0 "m/s")^2)$

$= 10.7 "J"$

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

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

$= frac{10.7 "J"}{72 "W"}$

$= 0.148 "s"$

An electric toy car with a mass of 3 kg3kg3 kg is powered by a motor with a voltage of 9 V9V9 V and a current supply of 8 A8A8 A. How long will it take for the toy car to accelerate from rest to 8/3 m/s83ms8/3 m/s?