the velocity of a particle of mass m initially atrest at the origin varies with

Question

the velocity of a particle of mass m initially atrest at the origin varies with distance x as v(x) =bx where inNot = 1. Assume that at t = 0 the particle is at rest atthe orgin. (a) Find the force acting on the particle,F(x). (b) Determine x(t). (c) Obtain anexpression for the force as a function of time, F (t). hint: the answer to (a) isF=mb2x2-1 the velocity of a particle of mass m initially atrest at the origin varies with distance x as v(x) =bx where inNot = 1. Assume that at t = 0 the particle is at rest atthe orgin. (a) Find the force acting on the particle,F(x). (b) Determine x(t). (c) Obtain anexpression for the force as a function of time, F (t). hint: the answer to (a) isF=mb2x2-1

Explanation / Answer

a) force = mass*acceleration acceleration = dv/dt = d[bx]/dt =b**x-1*[dx/dt]   by power rule andthen chain rule a = b**x-1*[dx/dt] =b**x-1*v =b**x-1*b*x=b2*x2-1 F = m*a = mb2*x2-1 b) v = dx/dt = bx dx/x = b*dt 1/x-1 = b*t    =>  x(t) = (1/bt)1/[-1] c) Sub x into Force F = m*a = mb2*x2-1 =mb2**[(1/bt)1/[-1]]2-1 F =m*b2**(1/bt)[2-1]/[-1]

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