Mathematics 1560 Lecture 13: c3s4
Document Summary
The instantaneous rate of change of f with respect to x at x0 is the derivative f (x0) = lim h 0 f (x0 + h) f (x0) h provided the limit exists. Velocity (instantaneous velocity) is the derivative of position with respect to time. If a body"s position at time t is s = f (t), then the body"s velocity at time t is v(t) = ds dt. T 0 f (t + t) f (t) Speed = |v(t)| = (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) ds dt (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) Acceleration is the derivative of velocity with respect to time. If a body"s position at time t is s = f (t), then the body"s acceleration at time t is a(t) = dv dt d2s dt2 . Jerk is the derivative of acceleration with respect to time: j(t) = da dt d3s dt3 . No- tice what this implies that the accelerations are.
