Question

A body of mass $2kg$ has an initial speed of $5m/s$. A force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. The final speed of the body is

• A. $9.25m/s$
• B. $5m/s$
• C. $14.25m/s$
• D. $4.25m/s$

Answer 1

The correct option is C $14.25m/s$

According to Newton’s second law, force is equal to rate of change of momentum.

$F=\frac{mv-mu}{t}$
$mv-mu=F\times t$

which is given by the area under the $F-t$ graph.


Area under the graph $=\frac{1}{2}\times (2\times 4)+(2\times 4)+\frac{1}{2}\times \left(\right(4+2.5)\times 0.5)+(2\times 2.5)$

$=18.625kgm/s$

Given $u=5m/s$ and $m=2kg$
$2v-10=18.625$
$\Rightarrow v=14.31m/s$