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Question

# The velocity (V) versus displacement (S) graph of a particle moving in a straight line is as shown in the figure. Given Vo=4 m/s and So=20 m. At what displacement do velocity and acceleration have the same magnitudes?

A
At S=5 m
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B
At S=10 m
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C
At S=30 m
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D
None of these
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Solution

## The correct option is D None of these For S=0 to S=So V=VoSSo and a=V2oS2oS If velocity and acceleration have same magnitudes, V=a⇒Vo=So which is not possible with the given values of Vo and So. For S=So to S=2So V=−VoSoS+2Vo=−420S+2Vo =−S5+8 a=V2oS2o.S−2V2oSo=(420)2.S−2×4240 =S25−85 If velocity and acceleration have same magnitudes, V=a⇒−S5+8=S25−85 ⇒S=40 m

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