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 $m{s}^{- 1}$ ) of the particle after it has travelled a distance of $30m$ . The initial velocity is $10\text{m}{s}^{- 1}$ .

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

m{s}^{- 1}

) of the particle after it has travelled a distance of

30m

. The initial velocity is

10\text{m}{s}^{- 1}

.

A particle moves along a straight line with a variable acceleration given in the acceleration-displacement (a - S)

Quantrex Academy · Accepted Answer

Correct answer: 20

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 = 20m s ^ - 1

A particle moves along a straight line with a variable acceleration...

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