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Q.

The acceleration of particle moving rectilinearly, varies with time as shown.
 Question Image
Calculate the displacement of the particle in the interval from t=2s to t=4s. Assume that v=0, x = 0 at t=0.
 

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a

10m

b

3.33m

c

6.67m

d

5m

answer is B.

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Detailed Solution

From the graph a=2t-2

⇒∫0vdv=∫0t(2t−2)dt⇒v=t22t
∫0vdx=∫24(t2−2t)dt{∵v=dxdt}⇒x=(t33−t2)|42=(643−16−83+4)m
⇒x=6.67 m
 

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