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What is Acceleration Help (page 2)

By — McGraw-Hill Professional
Updated on Oct 25, 2011

What is Acceleration? Practice Problems

How Things Move HOW ACCELERATION IS DETERMINED

Fig. 15-9. Illustration for Practice 1-5.

Practice 1

Suppose two objects, denoted by curves A and B in Fig. 15-9, accelerate along straight-line paths. What is the instantaneous acceleration a inst at t = 4 seconds for object A?

Solution 1

The acceleration depicted by curve A is constant, because the speed increases at a constant rate with time. (That’s why the graph is a straight line.) The number of meters per second squared does not change throughout the time span shown. In 10 seconds, the object accelerates from 0 m/s to 10 m/s; that’s a rate of speed increase of one meter per second per second (1 m/s 2 ). Therefore, the acceleration at t = 4 seconds is a inst = 1 m/s 2 .

Practice 2

What is the average acceleration a avg of the object denoted by curve A in Fig. 15-9, during the time span from t = 2 seconds to t = 8 seconds?

Solution 2

Because the curve is a straight line, the acceleration is constant; we already know it is 1 m/s 2 . Therefore, a avg = 1m/s 2 between any two points in time shown in the graph, including the two points corresponding to t = 2 seconds and t = 8 seconds.

Practice 3

Examine curve B in Fig. 15-9. What can be said about the instantaneous acceleration of the object whose motion is described by this curve?

Solution 3

The object starts out accelerating slowly, and as time passes, its instantaneous rate of acceleration increases.

 

Practice 4

Use visual approximation in the graph of Fig. 15-9. At what time t is the instantaneous acceleration a inst of the object described by curve B equal to 1 m/s 2 ?

Solution 4

Use a straight-edge to visualize a line tangent to curve B whose slope is the same as that of curve A. Then locate the point on curve B where the line touches curve B. Finally, draw a line straight down, parallel to the speed ( v ) axis, until it intersects the time ( t ) axis. Read the value off the t axis. Here, it appears to be about t = 6.3 seconds.

Practice 5

Use visual approximation in the graph of Fig. 15-9. Consider the object whose motion is described by curve B. At the point in time t where the instantaneous acceleration a inst is 1 m/s, what is the instantaneous speed, v inst , of the object?

Solution 5

Locate the same point that you found in Problem 15-12, corresponding to the tangent point of curve B and the line parallel to curve A. Draw a horizontal line to the left, until it intersects the speed (v) axis. Read the value off the v axis. In this example, it looks like it’s about v inst = 3.0 m/s.

Find practice problems and solutions for these concepts at the Movement Practice Test.

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