Q.

A body with mass  2kg moves in one direction in the presence of a force which is described by the potential energy graph passing through (2,6) as shown. If the body is released from rest at  x=2m, then it speed when it crosses x=5m is: 

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a

zero

b

1m/s

c

3m/s

d

2m/s

answer is C.

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Detailed Solution

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 From x=2m to x=3.5m From, y=mx+cslope=0-63.5-2=-4y2-00-3.5=-4y2=14

U1=4x+14F1=dU1dx=+4NW1=+4×(3.52)=+6J From, x=3.5m to x=4.5mslope=2-04.5-3.5=2y2-00-3.5=2y2=-7U2=+2x-7F2=dU2dx=2NW2=2×(4.53.5)W2=2J

Work done from  4.5 m  to  5 m=0

12mv2=W1+W212×2×v2=62=4v=2m/s

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A body with mass  2kg moves in one direction in the presence of a force which is described by the potential energy graph passing through (2,6) as shown. If the body is released from rest at  x=2m, then it speed when it crosses x=5m is: