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Question

# A particle is moving along a straight line along the positive x-axis such that its speed is inversely proportional the the distance from origin [Vα1x⇒v=kxwhereKistheproportionalityconstant] At r = 0 the particle is at point A(x0,0) and moving along the positive x-axis with speed V0m/s The graph of motion of the particle for 1/V versus x ( distance from origin) A to B

A
The time interval of motion from point A to point B is 12.50 sec
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B
The time interval of motion from point A to point B is 18.75 sec
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C
The proportionally constant k is 10m2/s
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D
The proportionally constant k is 20m2/s
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Solution

## The correct options are A The time interval of motion from point A to point B is 18.75 sec C The proportionally constant k is 10m2/sGiven : v=kxFrom the graph, v∣∣∣A=2 m/s∴ 2=k5 ⟹k=10m2/sAlso dxdt=kx ⟹ ∫205xdx=∫t0kdt where k=10m2/s∴ x22∣∣∣205=10×t∣∣∣t0∴ 202−522=(10)t ⟹t=18.75 s

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