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Chapter 3Acceleration and Free Fall
direction it is going, and a coordinate system is shown at the bottom of each
figure. In each case, figure out the plus or minus signs of the velocity and
acceleration. It may be helpful to draw a v-t graph in each case.
x
x
x
x
(a)(b)
(c)(d)
3.4Varying Acceleration
So far we have only been discussing examples of motion for which the
v-t graph is linear. If we wish to generalize our definition to v-t graphs that
are more complex curves, the best way to proceed is similar to how we
defined velocity for curved x-t graphs:
definition of acceleration
The acceleration of an object at any instant is the slope of the tangent
line passing through its v-versus-t graph at the relevant point.
Example: a skydiver
Question: The graphs show the results of a fairly realistic
computer simulation of the motion of a skydiver, including the
effects of air friction. The x axis has been chosen pointing down,
so x is increasing as she falls. Find (a) the skydiver’s
acceleration at t=3.0 s, and also (b) at t=7.0 s.
Solution: I’ve added tangent lines at the two points in question.
(a) To find the slope of the tangent line, I pick two points on the