Question

A body of mass $5\text{kg}$ is moving along a straight line with a velocity of $2{\text{ms}}^{-1}$. A variable force $F$ started acting on it for a time period of $0.5s$ as shown in force - time curve. The final velocity of the block is

• A. $2{\text{ms}}^{-1}$
• B. $2.2{\text{ms}}^{-1}$
• C. $2.5{\text{ms}}^{-1}$
• D. $2.7{\text{ms}}^{-1}$

Answer 1

The correct option is C $2.5{\text{ms}}^{-1}$


Impulse = Area under F - t curve
$=A_1-A_2=\frac{1}{2}(0.4+0.2)\times 10-5\times 0.1$
$=3-0.5=2.5\text{N -s}$
$m(v-u)=2.5$
$5(v-2)=2.5,v=2.5{\text{ms}}^{-1}$
$\therefore \left(c\right)$

Why this question? "Application of graph: Impulse is given by area under the F-t curve ." Caution : $A_2$ is negative as force retards the motion