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Q.

The velocity-displacement graph describing the motion of a bicycle is shown in the figure.

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The acceleration-displacement graph of the bicycle’s motion is best described by

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a

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b

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c

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d

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answer is A.

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Detailed Solution

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Given velocity – displacement graph equation of line AB
v=(5010)(2000)×(x0)+10(0x200)v=40200×x+10v=x5+10 .(i)
Differentiate equation (i) w.r.t.x dvdx=15(ii)
Acceleration, a=dvdt=dvdx×dxdt=vdvdx
a=x5+10×15 (Using (i) and (ii)
a=x25+2ms2, At x=0,a=2ms2
It is straight line till x = 200.
For x>200, V = constant, a = 0.
Therefore, most appropriate option will be 

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The velocity-displacement graph describing the motion of a bicycle is shown in the figure.The acceleration-displacement graph of the bicycle’s motion is best described by