Question

Kinetic energy required to accelerate a car from $10m{s}^{-1}$ to $20m{s}^{-1}$ compared with that required to accelerate it from $0$ to $10m{s}^{-1}$ is:

• A. Twice
• B. Three times
• C. Four times
• D. Same

Answer 1

The correct option is B Three times

We know, Difference in K.E = $\frac{1}{2}m(v^2-u^2)$

The difference of K.E in the first case is $\frac{1}{2}\times m\times ({20}^2-{10}^2)=\frac{1}{2}\times m\times (400-100)=\frac{1}{2}\times m\times 300$

The difference in K.E. in the second case is$\frac{1}{2}\times m\times ({10}^2-0^2)=\frac{1}{2}\times m\times (100-0)=\frac{1}{2}\times m\times 100$

$\frac{K.E_1}{K.E_2}=\frac{3}{1}$

So, the answer is 3 times.