A body of mass $2 k g$ has an initial speed of $5 m / s$ . 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

9.25 m / s

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5 m / s

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14.25 m / s

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4.25 m / s

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Solution

The correct option is C $14.25 m / s$
According to Newton’s second law, force is equal to rate of change of momentum.

$F = \frac{m v - m u}{t}$
$m v - m u = F \times t$

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

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

$= 18.625 k g m / s$

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

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