Question

A particle moves along a straight line with a variable acceleration given in the acceleration-displacement $\left(a - S\right)$ curve as shown in the figure. Determine the velocity (in $ms^{- 1}$ ) of the particle after it has travelled a distance of $30m$ . The initial velocity is $10\text{m }s^{- 1}$ .

Answer 1

Area under curve is $=\frac{1}{2}\times 10\times 30$
$=150$ ……..(i)
Area under the curve is also equal to $=\frac{v^{2} - u^{2}}{2}$ …….(ii)
From (i) and (ii)
$\frac{1}{2}\left(v^{2} - u^{2}\right)=150$
$\left(v^{2} - u^{2}\right)=300$
$v^{2}=u^{2}+300$
$v^{2}=\left(10\right)^{2}+300$
$v=\sqrt{400}=20\text{m }s^{- 1}$