(a) Explain in words the mathematical relationship between displacement, velocity and acceleration. (6 marks) The velocity of a point on a mechanism is described (with respect to time) by the vector v = bt3e-Bti+ In(t-2vx) i Therefore, by considering motion in the x- and y-direction independently: Vx (t) = bt3e-Bt Vy (t) = In(t-2Vx) where B and b are constants. (b) Being careful to show all of your reasoning, demonstrate that: (i) the component of acceleration in the x-direction, ax, is given by ax = bthe-Bt(3 - Bt) (ii) the component of acceleration in the y-direction, ay, is given by ay B + 1 (12 marks) (c) Using the above results, find the time and magnitude of the maximum velocity in terms of B and b in the: (i) x-direction (ii) y-direction