Question

The particle moves in rectilinear motion as given in the acceleration – displacement $(a-s)$ curve shown in the figure. Determine the velocity after the particle has travelled $30\text{m}$, if the initial velocity is $10\text{m/s}$.

• A. $10\text{m/s}$
• B. $40\text{m/s}$
• C. $20\text{m/s}$
• D. $60\text{m/s}$

Answer 1

The correct option is C $20\text{m/s}$

As we know that,
$a=v\frac{dv}{ds}$
$\Rightarrow {\int }_{10}^{v}vdv={\int }_0^{30}ads$
$\Rightarrow {\int }_{10}^{v}vdv=$ Area under $a-s$ graph
$\Rightarrow {\left[\frac{v^2}{2}\right]}_{10}^v=\frac{1}{2}\times 30\times 10=150$
$\Rightarrow v^2-100=300$
$\Rightarrow v=20\text{m/s}$