A particle of mass m moves in a straight line under the influence of a consevati

Question

A particle of mass m moves in a straight line under the influence of a consevative force F = k/x3 , where k is a positive constant and x the coordinate on the line.

a) If the particle starts from a position xo > 0 moving towards the origin with speed vo, find the smallest distance from the origin a that the particle will reach.

b) After a long time, the particle will be moving away from the origin with a speed approaching vf . Calculate vf .

c) Write an equation for dx/dt and solve it to obtain x(t) using the appropriate initial conditions as determined in part (a).

d) Find the time t at which the particle will reach its shortest distance from the origin a as in part (a).

Explanation / Answer

m(d^2X/dt^2) = K/X^3

simply integrate this eqn....you will find eqn for x

now for velocity

v = dx/dt

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