[A] 1D Projectile Motion

   (1) Choose values for x0, v0, and a so that the particle starts
       on top of a building and is thrown downward

        Example:
        m  = 1.0
        g  = 9.8

        x0 = -3
        v0 = +3
        a  = -g

        x  = x0 + v0 * t + a * t^2
        v  = v0 + a * t

   (2)  Plot x and v for various (3 different)  initial values:

        Plot[{x,v},{t,0,10}]

[B] 2D Projectile Motion

   (1) Choose values |v0|, ax, and ay, x0, and y0, theta
       So that the object is launched upwards and goes the maximum distance for a speed of 100.

       Clear[x]
       Clear[x0]
       Clear[v0]

       x0     = 0
       y0     = 0
       ax     = 0
       ay     = -g
       v0     = 10.
       theta  = 10.Degree

       vx0    = v0 * Cos[theta]
       vy0    = v0 * Sin[theta]

       x      = x0 + vx0 * t + (1/2) * ax * t^2
       y      = y0 + vy0 * t + (1/2) * ay * t^2

       ParametricPlot[{x,y},{t,0,10}]

[C] Force, Potential Energy and Work 

   (1) Find a U(x) which has both stable and unstable equilibrium points:
   
       Example:
   
        U   =  x^2
        F   =  -D[U,x]
        Plot[{U,F},{x,-1,1}]
   
   (2) Check that U==-W where W is the integral of Fdx
   
        W   = Integrate[F,x]
        U  == -W

   (3) Find the equilibrium points of the potential. You have to tell Mathematica
       roughly at what x-value to look (here, I give it the value "1").

        FindMinimum[U,{x,1}]
        FindMaximum[U,{x,1}]