Lesson 1.3: Average Velocity
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Lesson 1.3: Average Velocity
Imagine you are a pilot flying from Westlock to a fly-in breakfast in Lacombe. To know that you are going to get to your destination at a certain time, you need to keep track of both speed and direction of the airplane’s motion. You might be travelling fast enough to get there on time; but if you are going in the wrong direction, you will still miss out on the breakfast in Lacombe.
This lesson has you working with vector quantities as opposed to just scalar quantities. The concept of vector addition is introduced.
Recall: Scalar and Vector Quantities
Distance is measured along a path without regard to direction. The distance traveled along the blue line on the might might be 3.5 km.
Displacement is the measure from the stating point to the ending point. The displacement measured by the green line might be represented by 1.7 km S 70° E. The word position is used to describe the displacement from the stating point to the endpoint.
Displacement is the measure from the stating point to the ending point. The displacement measured by the green line might be represented by 1.7 km S 70° E. The word position is used to describe the displacement from the stating point to the endpoint.
- Read pages 179 to 181, up to "average Velocity". Work through Example problem 1.5 and check the solution. Do Practice Problem 14 and check. Work through Example Problem 1.6 and do Practice Problem 15. there is an assignment problem like this. Check the “Practice Answers”
Average velocity is the total displacement over the total time. Remember that an expression of average velocity includes direction.
The average velocity of an object in motion is an indication of not only how fast the object changes position, but the direction of this change. A pilot must always be aware of the airplane’s average velocity. This is not easy considering that the velocity will be determined by both the heading (speed and direction) of the airplane, and the speed and direction of the wind. It is possible that the heading of an airplane is 80 km/h North and the wind is blowing 80 km/h South, so the average speed is zero.
If vector A is 5 km East, and vector B is 3 km West, we can add them mathematically:
In this example East is considered positive and West is negative.
- Read pages 181 and 182. Work through the Example Problems.
Vector Addition
Vector quantities can be added (and subtracted) graphically and mathematically. It is good to have an understanding of how vectors are added graphically. Two or more vector can be added graphically by connecting them head to tail and drawing the resulting rector. The simplest case of this is adding vectors in one dimension. The diagram below adds vector A to vector B. the resultant vector is the bold arrow.Resultant vector: ADLC
5 km E + 3 km W or 5 km +«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«maction actiontype=¨argument¨»«mrow»«/mrow»«/maction»«mo»-«/mo»«/msup»«/math»3 km = 2 km W
- Read page 183 - 184. Do Practice Problems 17 and 18, then check the “Practice Answers”
- Read “1.3 Summary” on page 185 of the textbook. Then, complete questions 2 and 3 and check your answers. Do 4 and 5 if you feel you need more practice. Check your answers in the “Practice Answers” .