Velocity (V) versus displacement (S) graph of a particle moving in a straight line is as shown in the figure. Given Vo=4m/s and So=20m.
Corresponding acceleration (a) versus displacement (S) graph of the particle would be
A
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B
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C
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D
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Solution
The correct option is A From S=0 to S=So velocity is given by, V=VoSoS⇒dVdt=VoSo(dSdt) ⇒Acceleration,a=VoSo(VoSoS) ⇒a=V2oS2o.S ⇒a∝S
From S=SotoS=2So, velocity is given by V=−VoSoS+2Vo dVdt=−VoSo(dSdt) Accleration,a=−VoSo(−VoSoS+2Vo)=V2oS2o.S−2V2oSo At S=So,a=−V2oSoand atS=2So,a=0
Hence, graph (a) is correct.