**What is Speed and Velocity Practice Problems**

Review the concept of speed at What is Speed and Velocity Help**. **** **

**Fig. 15-5.** Illustration for the following practice problems.

**Practice 1 **

Look at the graph of Fig. 15-5. Curve A is a straight line. What is the instantaneous speed *v* _{inst} at *t* = 5 seconds?

**Solution 1 **

The speed shown by curve A is constant. You can tell because the curve is a straight line. The number of meters per second does not change. In 10 seconds, the object travels 20 meters; that’s 20/10 — 2.0 meters per second. Therefore, the speed at *t* = 5 seconds is *v* _{inst} = 2.0 meters per second.

**Practice 2 **

What is the average speed v _{avg} of the object denoted by curve A in Fig. 15-5, during the time span from *t* = 3 seconds to *t* = 7 seconds?

**Solution 2 **

Because the curve is a straight line, the speed is constant; we already know it is 2.0 meters per second. Therefore, v _{avg} = 2.0 meters per second between any two points in time shown in the graph.

**Practice 3 **

Examine curve B in Fig. 15-5. What can be said about the instantaneous speed of the object whose motion is described by this curve?

**Solution 3 **

The object starts out moving relatively fast, and the instantaneous speed decreases with the passage of time.

**Practice 4 **

Use visual approximation in the graph of Fig. 15-5. At what time *t* is the instantaneous speed *v* _{inst} of the object described by curve B equal to 2.0 meters per second?

**Solution 4 **

Use a straight-edge to visualize a line tangent to curve B whose slope is the same as that of curve A. That is, find the straight line, parallel to line A, that is tangent to curve B. Then locate the point on curve B where the line touches curve B. Finally, draw a line straight down, parallel to the distance ( *d* ) axis, until it intersects the time ( *t* ) axis. Read the value off the *t* axis. In this example, it appears to be approximately *t* = 3.2 seconds.

**Practice 5 **

Use visual approximation in the graph of Fig. 15-5. Consider the object whose motion is described by curve B. At the point in time t where the instantaneous speed v _{inst} is 2.0 meters per second, how far has the object traveled?

**Solution 5 **

Locate the same point that you found in Problem 15-7, 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 distance ( *d* ) axis. Read the value off the *d* axis. In this example, it looks like it’s about *d* = 11 meters.

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