A particle of mass 3 kg moves along the positive x -axis under the influence of a constant force. The variation of the square of its velocity ( v^2 ) with position ( x ) is represented by a straight line passing through the origin and the point (4 m , 16 m ^2/ s ^2) . The magnitude of the force acting on the particle is :

Step-by-step solution

The graph of v^2 versus x is a straight line passing through (0,0) and (4, 16) . The slope of this line is k = 16 - 0 4 - 0 = 4 m/s ^2 . The equation of the line is v^2 = 4x . Differentiating both sides with respect to x gives: 2v dv dx = 4 Since acceleration a = v dv dx , we have: 2a = 4 a = 2 m/s ^2 The magnitude of the constant force is: F = ma = 3 2 = 6 N Answer: 6 N