4.2 - Acceleration in two dimensions
Analyzing acceleration in two dimensions is analogous to analyzing velocity in two
dimensions. Velocity can change independently in the horizontal and vertical
dimensions. Because acceleration is the change in velocity per unit time, it follows that
acceleration also can change independently in each dimension.
The cannonball shown to the right is fired with a horizontal velocity that remains
constant throughout its flight. Constant velocity means zero acceleration. The
cannonball has zero horizontal acceleration.
The cannonball starts with zero vertical velocity. Gravity causes its vertical velocity to
become an increasingly negative number as the cannonball accelerates toward the
ground. The vertical acceleration component due to gravity equals í9.80 m/s^2.
As with velocity, there are several ways to calculate the acceleration and its
components.
The average acceleration can be calculated using the definition of acceleration, dividing
the change in velocity by the elapsed time. The components of the average acceleration
can be calculated by dividing the changes in the velocity components by the elapsed
time. These equations are shown in Equation 1. Instantaneous acceleration is defined
using the limit as ǻt gets close to zero.
If the overall acceleration is known, in both magnitude and direction, you can calculate
itsx and y components by using the cosine and sine of the angle ș that indicates its
direction. These equations are shown in Equation 2.Acceleration in two dimensions
Velocity can vary independently in x,y
dimensions
Change in velocity = acceleration
Acceleration can also vary
independentlya = acceleration, v = velocity
ǻt = elapsed time
ǻvx,ǻvy = velocity components
(^68) Copyright 2000-2007 Kinetic Books Co. Chapter 04