Question

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

• A. $8\text{m}$
• B. $10\text{m}$
• C. $12\text{m}$
• D. $14\text{m}$

Answer 1

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

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