A vehicle travels in a fixed direction at a velocity v(t) that varies with time as follows: t < t t v(t) = At v(t)=CB(t-t) v(t) = v. Here A, B, C and v2 are constants. (a) Find A. B and C such that both the velocity and acceleration are continuous at t = t and t = t. (b) Sketch the velocity and acceleration as a function of time. (c) Find the total distance travelled between t = 0 and t = t3, where t > 12. [3] [3] [4]