Acceleration versus velocity graph of a particle moving in a straight line starting from rest is shown in the figure below.
How will the graph representing the variation of velocity with time look like?
The above graph implies that acceleration is decreasing linearly with increase in velocity. This means -
v = ma where m is slope of the line given in the figure.
But we also know that a = dv/dt. Replace a with v/m, we get
v/m = dv/dt
=> dt = m dv/v
Integrate on both the sides
t = m In(v) + C [here In v is log with base e]
=> v will be exponential with respect to t.
answered Mar 01 '12 at 23:46