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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