Image below. Save image for a better view. A particle moves on the positive x ax

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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. Calculate the velocity in the limit that t approaches infinity. [Data: m = 0.31 kg; k = 1.56 Nm2; x0 = 1.7 m] 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 - The units of force are Newtons, or kilogram-meter/second^2. If we were to factor out mass and then integrate force, we would get mass*velocity. Simply integrate that expression and multiply by the supplied mass and you're good to go! :)

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