Instruction 1-2

Pre-test		Post-test
Q&A	The Physics of Motion	Q&A

Motion,  Distance and Time Relationships | Speed and Velocity

Speed

Like any other physical phenomena, we are interested in measuring the rate of motion of any object. It is identified by its speed. The speed of an object indicates that how fast the object is moving, or how much of its motion occurs within a certain time interval. We know that the more speed an object has, the faster it moves. To determine the average speed of an object we apply two factors: Elapsed Time and Distance.
The average speed of an object is the ratio of the distance to the elapsed time it took to travel that distance. In other words, the average speed or average rate of motion of an object is determined by the distance traveled divided by the elapsed time.
Average speed is a scalar quantity. A scalar quantity is identified by simply its measure and no other specification. For example, the capacity of a container is a scalar quantity, but the magnitude of the force you apply to move a box is not. It is called a vector quantity because it has two specifications, force and the direction of the force.
 
For example, if a car travels the distance between two towns which are 120 miles away in 2 hours, then the average speed of the car through this movement is miles per hour.We usually denote the average speed of an object by s. Then using the notations for the distance and elapsed time, the average speed can be defined by the formula below:

We can also develop the following formulas by cross multiplying or reversing the formula above.

Practice 3. John rides his bike to school everyday. The distance between his home and the school is 3 miles. It takes him 12 minutes to ride this distance everyday. What is his average speed in miles per hour?Solution
First we need to convert the elapsed time measured in minutes to the equivalent time measured in hours.Practice 4. A train’s average speed during a 45-mile trip is 65 miles per hour. How long did it take the train to complete this distance?Solution. We are given
Elapsed Time = ∆t
Speed = 65 miles per hour
Distance = 45 miles
Replacing these values in the formula, we get

Average Velocity

When the ratio of the displacement of an object to the elapsed time is calculated, the result is called the average velocity of the object in motion. Thus,
 

Showing the average velocity by v, displacement by d, and elapsed time by t, then the formula of the average velocity is as follows

In the figure below, a person runs from the point A through the courses AB, BC, and CD and stops at the point D within 3 minutes. His running distance is
25 ft. + 12 ft. + 20 ft. = 57 ft

Thus, d = 27 ft. So the average speed of the person is

But the displacement of this person is equal to the AD. That is, though the person though runs a very long distance, his displacement is very short, from A to D which is 13 ft. Thus, the average velocity of the person is

Practice 5. It takes a swimmer 24 seconds to swim across a river which is 56 ft. What is the average velocity of the swimmer?

Solution. Use the formula of the velocity as follows:

Practice 6. A cyclist travels a distance with average velocity of 66 miles per hour in 40 minutes. How long is the distance? Solution. Replace the measures given in the velocity formula and solve for d.
Before replacing the values, we must convert minutes to hours.

Now, replace the known values in the formula, and solve.

Video Instruction
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• “Old school” narration of concepts with motion and graphs (6:14)

Experiments for Home and Classroom

To see experiments related to the concepts of speed and velocity, see the following web pages:
http://cosmology.berkeley.edu/Education/ISTAT/cfpa/speed/speedweb.html

for Students, Parents and Teachers

Now let's do Practice Exercise 1-2 (top).

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