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 $F\left(t\right)$ in the x direction. The force $F\left(t\right)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5$ seconds is:

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

Answer 1

Answer: (C)

$5.06J$

Area under the $F-t$ graph gives the change in momentum of the block.

Area $A$ = Area of triangle ABO - Area of triangle DCO

$\therefore$ $A=\frac{1}{2}\left(4\right)\left(3\right)-\frac{1}{2}\left(2\right)\left(1.5\right)=4.5$ $Ns$

Initial momentum of the block $P_i=0$

Using $A=P_f-P_i$

$⟹$ $P_f=4.5$ $Ns$

Thus final kinetic energy of the block $K_f=\frac{P_f^2}{2m}$

$⟹$ $K_f=\frac{(4.5{)}^2}{2\left(2\right)}=5.06J$