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 fore F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

(F)t

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

Answer 1

The correct option is C 5.06 J

Area under the curve of F – t graph provides change in momentum of particle since
$Fdt=d\left(mV\right)\Rightarrow \int Fdt=\Delta mV$
$\Rightarrow p=4.5kgm{s}^{-1}$
$\text{Kinetic energy}=\frac{p^2}{2m}=\frac{{4.5}^2}{2\times 2}=5.06J$