Unit Kinematics Module Investigating One Dimensional Motion page 1 of 1 Acceleration The ratio of the change in velocity to the time interval over which it occurs is the v average acceleration a t The instantaneous acceleration is the average acceleration as t tends to zero v dv a lim t 0 t dt The first derivative of position with respect to time is velocity The first derivative of velocity with respect to time is acceleration In many physical situations the change in velocity per unit time or the average acceleration is v important a For example if the limousine s t velocity changes from 100 mph to 0 mph in 2 min the limousine has stopped at a stop sign If the limousine s velocity changes from 100 mph to 0 mph in just 0 5 s the limousine has been in an accident The acceleration at an instant in time is found by calculating the average acceleration over a diminishingly small time interval The instantaneous v dv m and its unit is 2 acceleration is a lim t 0 t dt s The first derivative of position with respect to time is velocity The first derivative of velocity with respect to time is acceleration The sign of acceleration may be somewhat counterintuitive at first In the first example the iguanodon accelerates to the right or in the positive direction In the second example he slows down as he moves in the negative x direction In this case his acceleration is in the positive direction since the change in his velocity is positive In the third example the iguanodon slows down as he moves in the positive x direction His acceleration is negative because the change in his velocity is negative www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1776 doc rev 03 22 2001
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