1. Kinematics = the study of Motion Kinematics = the study of Motion

2. Kinematics Sounds a bit scary doesn’t it? Kinematics means: ‘the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations.’ In this unit of work we will be studying motion using all of the above so we will be studying Kinematics!

3. Instantaneous Speed During a typical trip to school, your car or bus will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often. The speedometer of a car reveals information about the instantaneous speed of your car; that is, it shows your speed at a particular instant in time.

4. Average Speed The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure of the distance travelled in a given period of time. Suppose that during your trip to school, you travelled a distance of 5 kilometres and the trip lasted 0.2 hours (12 minutes). Kilometres

5. Average Speed The average speed of your car could be determined as Average Speed = av speed = distance travelled = 5km = 25kmh -1 time taken 0.2h time taken 0.2h On the average, your car was moving with a speed of 25 kilometres per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 kilometres per hour; yet on the average you were moving with a speed of 25 kilometres per hour. Kilometres

6. Your Turn! Can you design an experiment to determine your average speed when you are walking, running? Remember av. speed = distanced travelled time taken time taken

7. Constant Speed Moving objects don't always travel with erratic and changing speeds. Occasionally, an object will move at a steady rate with a constant speed. That is, the object will cover the same distance every regular interval of time. For example a car travelling on the F3 with cruise control set on 100kmh -1 (27.8ms -1 ) will travel at that constant speed. An object with a changing speed would be moving a different distance each second.

8. The data tables below depict objects with constant and changing speeds.

9. Velocity Velocity is like speed except that it has a direction. The average velocity is often computed using the equation:

10. Velocity and Vectors Velocity is a vector quantity, this means it has direction. When evaluating the velocity of an object, you must keep track of its direction. The task of describing the direction of the velocity vector is easy! The direction of the velocity vector is the same as the direction in which an object is moving. It does not matter whether the object is speeding up or slowing down, if the object is moving rightwards, then its velocity is described as being rightwards. If an object is moving downwards, then its velocity is described as being downwards. Thus an airplane moving towards the west with a speed of 600kmh -1 has a velocity of 600kmh -1, west.

11. Acceleration An often misunderstood quantity, acceleration has a meaning much different from the meaning sports announcers and other individuals associate with it. The definition of acceleration is: Acceleration is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity.

12. Constant and Non-Constant Acceleration Sometimes an accelerating object will change its velocity by the same amount each second other times it will vary. If an object is changing its velocity – whether by a constant amount or a varying amount – it is an accelerating object.

13. Calculating Acceleration The acceleration of any object is calculated using the equation: V - U

14. Don’t be Fooled An object with a constant acceleration should not be confused with an object with a constant velocity. Don't be fooled! An object with a constant velocity is not accelerating. Can you use the acceleration equation a = v – u to say why? t

15. A Task for You! Observe the animation of the three cars below. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer.

16. Answer You will notice that the green and blue cars accelerate at different rates. The red car is traveling at a constant speed. We could even say that the red car had a constant velocity. Why?

17. Another Task for You! Can you calculate the average acceleration for the object below? Draw a graph of this information with time on the x axis and velocity on the y axis. What shape does it have?

18. Motion Graphs One way of displaying motion is the use of graphs. Describing a journey made by an object is very boring if you just use words. As with much of science, graphs are more revealing.

19. Distance /Time Graphs Plotting distance against time can tell you a lot about a journey. Let's look at the axes: Plotting distance against time can tell you a lot about a journey. Let's look at the axes: Time always runs horizontally (the x-axis). The arrow shows the direction of time. The further to the right, the longer time from the start. Distance runs vertically (the y-axis). The higher up the graph we go, the further we are from the start. This object is moving at a constant speed. Why? Time (sec) Distance (m)

20. Observe the two cars below. The blue car starts "ahead of" the red car (which actually starts "off the screen"). Since the red car is moving faster, it eventually catches up with and passes the blue car. The lines would intersect for a distance vs. time graph; the fact that the red car passes the blue car means that there is an instant in which they occupy the same position. The two cars have the same position at seven seconds; yet they never have the same velocity at any instant in time.

21. For You To Do See if you can work out what is happening in the following distance time graph. Click on the boxes 1,2 and 3 after you answer each section to reveal the answer. Constant speed Stopped Slower constant speed than 1 back to start 1 2 3 Time (sec) Distance (m)

22. Velocity/Time Graph A velocity time graph can tell us about the acceleration of an object and how far it has travelled. Can you explain each section of the graph line? Time (sec) Velocity (ms -1 ) Constant acceleration Constant Velocity

23. Observe the velocity-time graphs for these two cars. The same red and blue cars from the previous question. Each car's motion is represented by a horizontal line, indicating a constant velocity. Observe that even though the cars pass each other, the lines on the velocity-time graphs do not intersect. Each car's motion is represented by a horizontal line, indicating a constant velocity. Observe that even though the cars pass each other, the lines on the velocity-time graphs do not intersect. Since the cars never have the same velocity, the lines on the velocity-time graph never cross.

24. For You To Do Can you explain each section of this graph? Click on the numbers as you answer each section. Did you know that by working out the area under this graph you can tell how far the object had gone? Fast Acceleration Constant Acceleration Constant Velocity -ve acceleration Time (sec) Velocity (ms -1 ) 1 2 3 4

25. What’s Happening Here? Can you work out what type of motion is happening here? Can you think of some where that this type of motion is occurs? Time (sec) Velocity ms -1 Non Constant Acceleration Click here.

26. Try this Quick Quiz - Data A blue car moving at a constant speed of 10 ms -1 passes a red car that is at rest. This occurs at a stoplight the moment that the light turns green. The clock is reset to 0 seconds and the velocity-time data for both cars are collected and plotted. The red car accelerates from rest at 4 ms -2 for three seconds and then maintains a constant speed. The blue car maintains a constant speed of 10 ms -1 for the entire 12 seconds.

27. Try This Quick Quiz - Questions Observe the motion and make meaning of the accompanying graphs to answer the following questions: What is the final velocity of a car that accelerates from rest at 4 m/s/s for three seconds? What is the displacement of each individual car after three seconds (consider a kinematic equation or the area of the velocity-time graph)? What is the slope of the line for the red car for the first three seconds? What is the displacement of each individual car after nine seconds (use the area of the velocity-time graph)? Does the red car pass the blue car at three seconds? If not, then when does the red car pass the blue car? When lines on a velocity-time graph intersect, does this mean that the two cars are passing by each other? If not, what does it mean?

28. Try This Quick Quiz - Answers Answers to questions: 12 ms -1 Red Car: Area of Triangle = 0.5xbxh = 0.5x(3 s)x(12 ms -1 ) = 18 m Blue Car: Area of Rectangle = b x h = (3 s)x(10 ms -1 ) = 30 m slope = rise/run = (12 ms -1 - 0 m/s)/3 s = 4 ms -2 Red Car: Area of Triangle + Area of Rectangle = 0.5xb1xh1 + b2xh2 = 0.5x(3 s)x(12 ms -1 ) +(9 s)x(12 ms -1 ) = 18 m + 72 m = 90 m Blue Car: Area of Rectangle = bxh = (9 s)x(10 ms -1 ) = 90 m No! The red car passes the blue car at 9 seconds. See animation and the result of the above question. No! When lines intersect on a v-t graph, it means that the two cars have the same velocity. When lines intersect on a p- t graph, it means that the two cars are passing each other.