A particle moves on the positive x axis (x > 0). A force F(x) = + k / x2 pushes

Question

A particle moves on the positive x axis (x > 0). A force F(x) = + k / x2 pushes the particle to larger x. Note that the force decreases to 0 as x approaches infinity. Suppose the initial conditions at t = 0 are x(0) = x0 and (dx/dt)0 = 0. Solve for the motion of the particle.
(A) Calculate the velocity in the limit that t approaches infinity.
[Data: m = 0.53 kg; k = 1.48 Nm2; x0 = 1.8 m ]


(B) Calculate the time t when v is equal to 0.50 v(?).
[Hint: The position (x) and time (t) can be related by parametric equations
x = x0 cosh2? = (x0/2){ cosh2?+ 1 }
and t = C { sinh2? + 2?}
where C is a constant, which you will need to determine.]

Explanation / Answer

A) V = dx/dt = 25 m/s B) t = 6 secs

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