Question

A block of mass $2 \, kg$ is having velocity $4\sqrt{5} \, m \, s^{- 1}$ in the positive x-direction at the origin. The only force acting on it is $F=\left(3 x^{2} - 12 x\right) \, N$ . Its velocity when it is at $x=2 \, m$ is

• A. $8 \, m \, s^{- 1}$
• B. $4 \, ms^{- 1}$
• C. $10\sqrt{24} \, m \, s^{- 1}$
• D. $20 \, ms^{- 1}$

Answer 1

Answer: (A)

From work energy theorem
$W=\Delta K$
$\displaystyle \int _{0}^{2} F d x = \frac{1}{2} m \left(v^{2} - u^{2}\right)$
$\displaystyle \int _{0}^{2} \left(3 x^{2} - 12 x\right) d x = \frac{1}{2} 2 \left(v^{2} - \left(4 \sqrt{5}\right)^{2}\right)$
$\left[x^{3} - 6 x^{2}\right]_{0}^{2}=v^{2}-80$
$8-24+80=v^{2}$
$v=8 \, m \, s^{- 1}$