JEE Main · PhysicsHard

$A particle moves along the x -axis such that its acceleration is a = - k x, where k is a positive constant. If the particle starts from rest at x = A, its velocity at x = 0 is:$

A. $A k$
B. $A / k$
C. $k A$
D. $k / A$

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Correct answer: A — $A k$

Solution

$The acceleration is v \frac{d v}{d x} = - k x .$
$Integrating both sides, \int_{0}^{v} v^{'} d v^{'} = \int_{A}^{x} - k x^{'} d x^{'} .$
$This gives \frac{v ^{2}}{2} = - \frac{k}{2} (x^{2} - A^{2}) .$
$At x = 0, \frac{v ^{2}}{2} = \frac{k A ^{2}}{2} .$
$Therefore, v = A k .$
$Hence the answer is (A).$

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A particle moves along the x-axis such that its acceleration is a=−kx, where k is a positive constant. If the particle starts from rest at x=A, its velocity at x=0 is:

Solution

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More Kinematics practice questions

$A particle moves along the x -axis such that its acceleration is a = - k x, where k is a positive constant. If the particle starts from rest at x = A, its velocity at x = 0 is:$