A body of mass $5 \mathrm{~kg}$ is moving in a straight line. The relation between its displacement and time…
A body of mass $5 \mathrm{~kg}$ is moving in a straight line. The relation between its
displacement and time is $\mathrm{x}=\left(\mathrm{t}^{3}-2 \mathrm{t}-10\right) \mathrm{m}$. What is the force acting on it at the end of 5 second?
$150 \mathrm{~N}$
$120 \mathrm{~N}$
$80 \mathrm{~N}$
$100 \mathrm{~N}$
Solution
A body of mass,
$\begin{aligned}
m &= 5 \, kg \\
x &= (t^{3}-2t-10)m
\end{aligned}$
$F$ after $t=5 \, sec$,
$\begin{aligned}
\frac{dx}{dt} &= v = 3t^{2} - 2 \\
\frac{dv}{dt} &= a = 6t \\
F &= ma = 5 \times 6t = 30 \times 5 \\
F &= 150 \, N
\end{aligned}$