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

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Area under curve is = 1 2 × 10 × 30 = 150 ……..(i) Area under the curve is also equal to = v 2 - u 2 2 …….(ii) From (i) and (ii) 1 2 v 2 - u 2 = 150 v 2 - u 2 =300 v 2 = u 2 + 300 v 2 = 10 2 + 300 v = 400 = 20 m s - 1

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