Question

Energy required to accelerate a car from $10m/s$ to $20m/s$ compared with that required to accelerate it frem $0$ to $10m/s$ is

• A. twice
• B. thrice
• C. four times
• D. same

Answer 1

Answer: (B)

$K{E}_1=\frac{1}{2}m\left(v_2^2-v_1^2\right)$
$\therefore K{E}_1=\frac{1}{2}m\left[(20{)}^2-(10{)}^2\right]$
$\Rightarrow K{E}_1=\frac{1}{2}m(400-100)$
$\Rightarrow K{E}_1=\frac{1}{2}m\times 300=150m$ ... (i)
$K{E}_2=\frac{1}{2}m\left[(10{)}^2-0\right]$
$\Rightarrow K{E}_2=\frac{1}{2}m\times 100=50m$ ... (ii)
From Eqs. (i) and (ii), we have
$K{E}_1=3K{E}_2$