An electric toy car with a mass of $6 k g$ $6 kg$ 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 $\frac{7}{2} \frac{m}{s}$ $7/2 m/s$ ?

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Answer 1 · 2016-03-20T02:24:59

$1.53 s$ $1.53 "s"$

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

$Δ KE = \frac{1}{2} m (v^{2} - v_{0}^{2})$ $Delta "KE" = 1/2 m (v^2 - v_0^2)$

$= 1/2 (6 "kg") ((7/2 "m/s")^2 - (0 "m/s")^2)$

$= 36.75 "J"$

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

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

$= frac{36.75 "J"}{24 "W"}$

$= 1.53 "s"$

An electric toy car with a mass of 6 kg6kg6 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 7/2 m/s72ms7/2 m/s?