AP Calculus Review Position, Velocity, and （美联社微积分复习的位置,速度,和）.pdf

* AP Calculus Review Position, Velocity, and Acceleration Teacher Packet AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this material. ® Copyright © 2008 Laying the Foundation , Inc., Dallas, TX. All rights reserved. Visit: Position, Velocity, and Acceleration Page 1 of 15 Session Notes Suppose an object is moving along a straight line, such as the x-axis, so that its position x , as a function of time t, on that line is given by y x (t ) . Average velocity of the object over the time interval t to t +Δt is given by x (t +Δt) −x(t) change in position , or . Δt change in time Instantaneous velocity of the object is the derivative of the position function x (t) with ′ respect to time. v(t) x (t) dx Speed is the absolute value of the velocity. Speed v(t ) . dt ′ ′′ Acceleration is the derivative of velocity with respect to time. a(t) v (t) x (t) ∫v(t) dt x(t) =+c , ∫a(t ) dt v(t) =+c Total distance traveled from time t t1 to t t2 is given by t 2 TDT ∫t v(t) dt .