Force is applied to a body of mass $2 \mathrm{~kg}$ at rest on a frictionless horizontal surface as shown in…
Force is applied to a body of mass $2 \mathrm{~kg}$ at rest on a frictionless horizontal surface as shown in the force against time $(\mathrm{F}-\mathrm{t})$ graph. The speed of the body after 1 second is
$7.5 \mathrm{~m} / \mathrm{s}$
$12.5 \mathrm{~m} / \mathrm{s}$
$10 \mathrm{~m} / \mathrm{s}$
$15 \mathrm{~m} / \mathrm{s}$
Solution
Area under the F-t graph gives change in momentum. Since the body is initially at rest, it gives the momentum of the body after 1 second.
$\begin{aligned}
& \text { Area }=10 \times 0.5+20 \times 0.5=5+10=15 \mathrm{~N}-\mathrm{s} \\
& \therefore \mathrm{mV}=15 \mathrm{~N}-\mathrm{s} \\
& \mathrm{V}=\frac{15}{\mathrm{~m}}=\frac{15}{2}=7.5 \mathrm{~m} / \mathrm{s}
\end{aligned}$
