Question

If velocity is reduced to $\frac{1}{3}$ of the initial velocity, the kinetic energy of a moving cart:

• A. becomes $3$ times
• B. remains same
• C. becomes $9$ times
• D. becomes $\frac{1}{9}$ times

Answer 1

Answer: (D)

becomes $\frac{1}{9}$ times

Initial kinetic energy$=K_1=\frac{1}{2}m{v}^2$
Final kinetic energy$=K_2=\frac{1}{2}\times m\times (\frac{1}{3}v{)}^2=\frac{1}{2}m\times \frac{1}{9}{v}^2$
$\therefore$ $K_2=\frac{1}{9}{K}_1$