A particle starts from rest and moves in a straight line so that t seconds after passing through a fixed-point P, its velocity v ms-1, is given by v = 5(1 – e^-t).

a. Find the velocity of the particle when t = ln 100.

b. State the value which v approaches as t becomes very large.

c. Find the acceleration of the particle when v = 4.

d. Sketch the velocity-time graph for the motion of the particle.