Section 6 : Average Speed (v av )and Average Velocity ( )

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1 Section 6 : Average Speed (v av )and Average Velocity ( ) Realistically, when objects move, their movement is almost always non-uniform. Turning, or obstacles force them to change. When we describe the trip of a moving object, the speed we often report is actually the average speed of the entire trip...the total distance covered, divided by the total time of the trip. v AV My average speed driving to HV - GB is 90 km / h. However, I cannot always drive at 90 km / h. Traffic, rest stops, turns, wildlife, etc. all cause me to change speed. If one was to describe how fast I was going at a particular point of my trip...then what we are describing is called an instantaneous speed...what I was doing at that one instant. This is what police measure with radar guns. It is your speed at a particular point in time. Formula: v av d t T T Most questions don t come right out and give you the total distance and total time. Rather, you ll be given clues in the question and you ll have to find total distance AND / OR total time yourself first...then plug everything into this formula to finish the question. A marathon runner in training runs 12 km from and then 22 km back to his house. If this takes 4.2 hours of running altogether, what is the runner s average speed?

2 A plane travelling non-stop travels at a speed of 750 km/h in 2.0 hours and then km/h for the remaining 5.0 hours. What is its average speed? Reminder... to find the average speed, you would first need to find the total distance AND then total time. To find total distance, you need to find d 1 and d 2. You must determine the distance covered during each leg of the trip...which means you need to perform 2 calculations, and add the two distances together before completing the question. Steven drives 20.0 km at a rate of 50.0 km/h and then 50.0 km at a rate of 40.0 km/h. Find Steven s average speed.

3 NOTE : As soon as you see any trip described in two parts, or legs, you should automatically realize you ll have to do TWO calculations, then combine the results into one final calculation that answers the question.

4 Average Velocity ( v AV ) Average velocity is the total displacement divided by the total time of the trip. The calculations for average velocity will be similar to those we just finished for average speed. You will have to be aware of the DIRECTIONS objects are moving in. Average velocity is a vector, so directions must be included in your workings and in your final stated answers. Average speed ( in most cases ) and average velocity will not give the same answer. Average speed involved the use of a total distance, but average velocity questions will use total displacement from start to finish. ( Remember...distance is the total length of a trips path, but displacement was the difference between your start point and your end point...no matter how much moving went on in between the two. ) For example, if your friends left their house, walked to the mall, then to McDonald s, and finally arrived at your house...they ve covered quite a distance. Any average speed question would use the length of their whole walk. An average velocity question would only consider the distance between the friend s house and yours, and their direction of your house relative to theirs...ignoring all the extra movement in between. Hit a home run... run through all three bases, make it to home plate... How would you find the average speed of the player? How would you find the average velocity?

5 A marathon runner in training runs 12 km [S] and then 27 km [N]. If this takes 4.2 hours of running altogether, what is the runner s average velocity? Remember movement in [N] or [E] direction is considered positive, movements [S] or [W] directions is considered negative. A plane travelling non-stop travels at a speed of 750 km/h [E] in 2.0 hours and then km/h [W] for the remaining 5.0 hours. What is its average velocity?

6 Steven drives 20.0 km [N] at a rate of 50.0 km/h [N], and then 50.0 km [S] at a rate of 40.0 km/h [S]. Find Steven s average velocity.