Question

The momentum $p$ of a particle changes with time according to the relation: $\frac{dp}{dt}=(10+2t)N$. If the momentum is zero at $t=0s$. What will the momentum in $Ns$ at $t=10s$

Answer 1

$\frac{dp}{dt}=10+2t$
$\int dp=\int (10+2t)dt$
$p=10t+\frac{2t^2}{2}+c$
$p=10t+t^2+c$
At $t=0;p=0\Rightarrow c=0$
$p=10t+t^2$
$p\text{at t = 10 s}$
$p=10\times 10+10\times 10=200Ns$