An electric toy car with a mass of $5 k g$ $5 kg$ is powered by a motor with a voltage of $4 V$ $4 V$ and a current supply of $2 A$ $2 A$ . How long will it take for the toy car to accelerate from rest to $3 \frac{m}{s}$ $3 m/s$ ?

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Answer 1 · 2016-11-13T02:03:04

Given

$V \to voltage supplied to motor of toy car = 4 V$ $V->"voltage supplied to motor of toy car"=4V$

$I \to current supplied to motor of toy car = 2 A$ $I->"current supplied to motor of toy car"=2A$

$v \to velocity gained by the car = 3 \frac{m}{s}$ $v->"velocity gained by the car "=3m/s$

$m \to mass of thecar = 5 k g$ $m->"mass of thecar "=5kg$

Let time taken to gain the velocity be t sec

Now $Power (P) = I \times V = 2 \times 4 W = 8 W$ $"Power"(P)=IxxV=2xx4W=8W$

The electrical energy spent in t sec will go to increase the velocity of the car from zero to $3 \frac{m}{s}$ $3m/s$ .

So

$P \times t = \frac{1}{2} \times m \times v^{2}$ $Pxxt=1/2xxmxxv^2$

$\Rightarrow 8 \times t = \frac{1}{2} \times 5 \times 3^{2}$ $=>8xxt=1/2xx5xx3^2$

$\Rightarrow t = \frac{5 \times 9}{2 \times 8} = 2.8125 s$ $=>t=(5xx9)/(2xx8)=2.8125s$

An electric toy car with a mass of 5kg5 kg is powered by a motor with a voltage of 4V4 V and a current supply of 2A2 A. How long will it take for the toy car to accelerate from rest to 3ms3 m/s?