Question

Velocity-time equation of a particle moving in a straight line is, $v=(10+2t+3t^2)$. Find displacement of particle during $t=1\text{sec}$, if it is given that position is $20\text{m}$ at time $t=0\text{sec}.$

• A. $12\text{m}$
• B. $48\text{m}$
• C. $32\text{m}$
• D. $64\text{m}$

Answer 1

The correct option is A $12\text{m}$

The given equation can be written as, $v=\frac{ds}{dt}=(10+2t+3t^2)$

$ds=(10+2t+3t^2)dt$

${\int }_{20}^{s}ds={\int }_0^t(10+2t+3t^2)dt$

$\Rightarrow s-20=[10t+t^2+t^3]{|}_0^1$

$s=20+12=32\text{m}$

but displacement during $1\text{sec}=32-20=12\text{m}$

Hence, option (d) is the correct answer.