Question

Acceleration of $10\text{kg}$ block is given as $a=(20-2t){\text{m/s}}^2$, where $t$ is in $\text{seconds}$. Find the average impulse imparted to the block during the time interval $0$ to $5$ $\text{sec}$.

• A. $1000\text{N.s}$
• B. $500\text{N.s}$
• C. $750\text{N.s}$
• D. $250\text{N.s}$

Answer 1

The correct option is C $750\text{N.s}$

Mass of block is $m=10\text{kg}$
Applying Newton's $2^{nd}$ law,
$F=ma=10(20-2t)$
$F=200-20t...\left(i\right)$
$\&\text{Impulse}=\int Fdt$
Impulse received by block from $t=0$ to $t=5\text{s}$ is given by,
$J={\int }_0^{5}Fdt...\left(ii\right)$
Substituting value of $F$ from Eq $\left(i\right)$ in Eq $\left(ii\right)$,
$J={\int }_0^5(200-20t)dt$
$J={[200t-10t^2]}_0^5$
$J=(1000-0)-(250-0)$
$\therefore J=750\text{N.s}$