# An electric toy car with a mass of 4 kg is powered by a motor with a voltage of 7 V and a current supply of 1 A. How long will it take for the toy car to accelerate from rest to 3/2 m/s?

Jun 18, 2016

$= \frac{9}{14} s$

#### Explanation:

Given

• $m \to \text{Mass of toy car } = 4 k g$
• $V \to \text{Applied voltage } = 7 V$
• $I \to \text{Current supply } = 1 A$
• $v \to \text{Velocity gained by toy car } = \frac{3}{2} m {s}^{-} 1$
• $\text{Let t be the time taken to gain the velocity " 3/2ms^-1 " from rest}$

Now assuming there is no loss of energy due to friction etc, we can apply conservation of energy to solve the problem.

$N o w P o w e r P = I \times V$

$\text{Electrical work done"="Gain in KE}$

$\implies P \times t = \frac{1}{2} \times m \times {v}^{2}$

$\implies I \times V \times t = \frac{1}{2} \times m \times {v}^{2}$

$\implies 1 \times 7 \times t = \frac{1}{2} \times 4 \times {\left(\frac{3}{2}\right)}^{2}$

$\implies t = \frac{9}{14} s$