Question

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

• A. $16\text{m}$
• B. $64\text{m}$
• C. $48\text{m}$
• D. $32\text{m}$

Answer 1

The correct option is D $32\text{m}$

The given equation can be written as,
$v=\frac{ds}{dt}=(10+2t+3t^2)$
$ds=(10+2t+3t^2)dt$
$\underset{20}{\overset{s}{\int }}ds=\underset{0}{\overset{t}{\int }}(10+2t+3t^2)dt$
$\because$ It is given that displacement is $20\text{m}$ at time $t=0$
$s-20={[10t+t^2+t^3]}_0^1$
$s=20+12=32\text{m}$