Higher Order Derivatives, Velocity and Acceleration Consider a down hill skier. What is the excitement of the sport? The position, 3 of a skier is described as a function of time, t. Therefore, 8 = f(t). Recall that the change in position, or velocity, v, at any time, t is the ie: v(t) = Note: speed is the absolute value of v(t). There is no If v(t) > 0 we say that the object is moving to the of the origin. If v(t) 0 when t 7 (moving to the right, away from the origin) V(t) 0 when t > 5 a(t)