Question

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F (t) in the x-direction. The force F (t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 s is

• A. 4.50 J
• B. 7.50 J
• C. 5.06 J
• D. 14.06 J

Answer 1

Answer: (C)

5.06 J

Answer 2

Area under F-t graph = momentum
\hspace30mm =p=\sqrt{2 \, km}
\therefore \, \, \, \, \, \, \, \, k=\frac{A^2}{2m} \hspace10mm (A = net area of F-t graph)
\hspace30mm =\frac{ \Bigg \\{ \big(\frac{4 \times 3}{2}\big)-\big(\frac{1.5 \times2}{2}\big)\Bigg \\}^2}{2 \times 2}
$\therefore$ The correct option is (c).