Physics and Speed Help (page 2)
Introduction to Speed
Speed is an expression of the rate at which an object moves relative to some defined reference point of view. The reference frame is considered stationary , even though this is a relative term. A person standing still on the surface of the Earth considers himself or herself to be stationary, but this is not true with respect to the distant stars, the Sun, the Moon, or most other celestial objects.
Speed Is A Scalar
The standard unit of speed is the meter per second (m/s). A car driving along Route 52 might have a cruise control device that you can set at, say, 25 m/s. Then, assuming that the cruise control works properly, you will be traveling, relative to the pavement, at a constant speed of 25 m/s. This will be true whether you are on a level straightaway, rounding a curve, cresting a hill, or passing the bottom of a valley. Speed can be expressed as a simple number, and the direction is not important. Thus speed is a scalar quantity. In this discussion, let’s symbolize speed by the lowercase italic letter v .
Speed can, of course, change with time. If you hit the brakes to avoid a deer crossing the road, your speed will decrease suddenly. As you pass the deer, relieved to see it bounding off into a field unharmed, you pick up speed again.
Speed can be considered as an average over time or as an instantaneous quantity. In the foregoing example, suppose that you are moving along at 25 m/s and then see the deer, put on the brakes, slow down to a minimum of 10 m/s, watch the deer run away, and then speed up to 25 m/s again, all in a time span of 1 minute. Your average speed over that minute might be 17 m/s. However, your instantaneous speed varies from instant to instant and is 17 m/s for only two instants (one as you slow down, the other as you speed back up).
How Speed Is Determined
In an automobile or truck, speed is determined by the same odometer that measures distance. However, instead of simply counting up the number of wheel rotations from a given starting point, a speedometer counts the number of wheel rotations in a given period of time. Knowing the wheel circumference, the number of wheel rotations in a certain time interval can be translated directly into meters per second.
You know, of course, that most speedometers respond almost immediately to a change in speed. These instruments measure the rotation rate of a car or truck axle by another method, similar to that used by the engine’s tachometer (a device that measures revolutions per minute, or rpm). A real-life car or truck speedometer measures instantaneous speed, not average speed. In fact, if you want to know the average speed you have traveled during a certain period of time, you must measure the distance on the odometer and then divide by the time elapsed.
In a given period of time t , if an object travels over a displacement of magnitude q at an average speed v avg , then the following formulas apply. These are all arrangements of the same relationship among the three quantities.
q = v avg t
v avg = q / t
t = q / v avg
Speed Practice Problems
Fig. 7.5 . Illustration for Problems 1 through 5.
Look at the graph of Fig. 7-5 . Curve A is a straight line. What is the instantaneous speed V inst at t = 5 seconds?
The speed depicted by curve A is constant; you can tell because the curve is a straight line. The number of meters per second does not change throughout the time span shown. In 10 seconds, the object travels 20 meters; that’s 20 m/10 s = 2 m/s. Therefore, the speed at t = 5 s is V inst = 2 m/s.
What is the average speed v avg of the object denoted by curve A in Fig. 7-5 during the time span from t = 3 s to t = 7 s?
Because the curve is a straight line, the speed is constant; we already know that it is 2 m/s. Therefore, V avg = 2 m/s between any two points in time shown in the graph.
Examine curve B in Fig. 7-5 . What can be said about the instantaneous speed of the object whose motion is described by this curve?
The object starts out moving relatively fast, and the instantaneous speed decreases with the passage of time.
Use visual approximation in the graph of Fig. 7-5 . At what time fis the instantaneous speed v inst of the object described by curve B equal to 2 m/s?
Take a ruler and find a straight 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 displacement ( q ) 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 s.
Use visual approximation in the graph of Fig. 7-5 . Consider the object whose motion is described by curve B . At the point in time t where the instantaneous speed v inst is 2 m/s, how far has the object traveled?
Locate the same point that you found in Problem 7-7, 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 displacement ( q ) axis. Read the value off the q axis. In this example, it looks like it’s about q = 11 m.
Practice problems of these concepts can be found at: Mass, Force, And Motion Practice Test
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