Question

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

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

Answer 1

The correct option is C three times

Energy required $E=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2=\frac{1}{2}m(v^2-u^2)$
where $m$ is the mass of the car.
Case 1 :
Initial speed $u=10m/s$
Final speed $v=20m/s$
Energy required $E_1=\frac{1}{2}m({20}^2-{10}^2)=150m$ Joules
Case 2 :
Initial speed $u=0m/s$
Final speed $v=10m/s$
Energy required $E_2=\frac{1}{2}m({10}^2-0)=50m$ Joules
$⟹E_1=3E_2$