An electric toy car with a mass of $2 k g$ $2 kg$ is powered by a motor with a voltage of $9 V$ $9 V$ and a current supply of $7 A$ $7 A$ . 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 · 2017-03-05T11:56:06

$0.036 s$ $0.036s$

Energy applied to the toy car is calculated as kinetic energy,

$E = \frac{1}{2} m v^{2} = \frac{1}{2} \times 2 \times {(\frac{3}{2})}^{2} = 2.25 J$ $E = 1/2mv^2 = 1/2 xx 2 xx (3/2)^2 = 2.25J$

We know that electrical power is

$P = I V$ $P = IV$

and mechanical power is

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

so

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

The question asks about the time taken, so rearrange for time,

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

and, putting in the values that we know,

$t = \frac{2.25}{9 \times 7} = 0.036 s$ $t = 2.25/(9 xx 7) = 0.036s$

An electric toy car with a mass of 2 kg2kg2 kg is powered by a motor with a voltage of 9 V9V9 V and a current supply of 7 A7A7 A. How long will it take for the toy car to accelerate from rest to 3/2 m/s32ms3/2 m/s?