An electric toy car with a mass of $3 k g$ $3 kg$ is powered by a motor with a voltage of $7 V$ $7 V$ and a current supply of $1 A$ $1 A$ . How long will it take for the toy car to accelerate from rest to $\frac{5}{3} \frac{m}{s}$ $5/3 m/s$ ?

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Answer 1 · 2017-03-05T16:14:37

$0.6 s$ $0.6s$

Electrical power is

$P = I V$ $P=IV$

and mechanical power is

$P = \frac{E}{t}$ $P = E/t$

so

$\frac{E}{t} = I V$ $E/t = IV$

We can work out $E$ $E$ by

$E = \frac{1}{2} m v^{2} = \frac{1}{2} \times 3 \times {(\frac{5}{3})}^{2} = 4.17 J$ $E = 1/2mv^2 = 1/2 xx 3 xx (5/3)^2 = 4.17J$

Rearrange the equation for time, which we want to find:

$t = \frac{E}{I V} = \frac{4.17}{7 \times 1} = 0.6 s$ $t = E/(IV) = 4.17/(7xx1) = 0.6s$

An electric toy car with a mass of 3kg3 kg is powered by a motor with a voltage of 7V7 V and a current supply of 1A1 A. How long will it take for the toy car to accelerate from rest to 53ms5/3 m/s?