Question

If speed is plotted along x-axis and Kinetic energy against y-axis, then the graph obtained has
a shape similar to that of
A. circle B. ellipse C. hyperbola D. parabola

Answer 1

   x =  v = speed   (instantaneous) 

   y = KE = 1/2 m  v²  = (m/2)  x²        instantaneous kinetic energy
      => x² =  2/m  y 

  This is in the form of    x² = (4a)  y    which is the standard equation for a parabola with y axis as the axis of the parabola and  (0,0) being the vertex of the parabola.  The directrix is given by  y = - a  = - 1/(2m)