Displacement and Velocity

1. Displacement and Velocity

2. Uniform Motion • Predicting the behaviour of moving objects can be very complex. Measuring and analyzing motion in the real world is a challenge, so scientists try to simplify their task. In Science 10 we only looked at UNIFORM motion. • Scientists try to model the behaviour of objects that move in straight lines at constant speeds as uniform motion because this can be easily analyzed. • Uniform motion: motion at constant velocity, with no change in speed or direction. When graphed it is linear.

3. Velocity for Uniform Motion • Velocity is a vector quantity which refers to "the rate at which an object changes its position." V = d__ t

4. Describing the direction of velocity (v) • The direction of the velocity vector is simply the same as the direction which an object is moving. We use square brackets to show the direction [right]. • 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. • Example: So an airplane moving towards the west with a speed of 300 km/hr has a velocity of 300 km/hr [West]. • Note that speed has no direction (it is a scalar) and velocity is simply the speed with a direction.

5. An airplane is moving towards the west with a speed of 300 km/hr. • 1) What is its velocity? • 2) If it goes for 50 km, how long does that take? • 3) How far would it go if it took 3.2 hours?

6. Physics teacher walking in circles again… • The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity. • The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. • However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s.

7. Distance Time Graphs • The slope of a distance time graph will tell us the Velocity of the object. • There are 3 possible cases:

8. 1. Horizontal Line • Slope of this line is zero. • The speed is zero. • If your speed is zero you are NOT MOVING.

9. 2. Uphill Line • Slope of this line is POSITIVE. • If your speed is positive you are MOVING FORWARD.

10. 3. Downhill Line • Slope of this line is NEGATIVE. • If your speed is negative you are MOVING BACKWARD.

11. Match the Graph to the Description • 1. The car is stopped. • 2. The speed of the car is decreasing. • 3. The car is coming back.

12. Velocity: position (Δdisplacement) vs. time graphsConsider a car moving with a constant, rightward (+) velocity of +10 m/s. • If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right. Note that a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph. • This is uniform motion!!!

13. The slope of a position-time graph is the velocity

14. Calculating average velocity from a position-time graph: • Examine the graph at the right which illustrates the motion of a car. Each section of the graph has a different slope representing individual velocities at that stage of the journey. • They can easily be calculated by finding individual slopes of that section of the graph. • The average velocity of the total graph or trip is found by using the beginning and end points.

15. Calculating average velocity from a position-time graph: • The velocity can easily be calculated by finding individual slopes of that section of the graph. • Ex: Section 1 slope = 12/0.4 = 30 • Velocity=30km/h [right] • The average velocity of the total graph or trip is found by using the beginning and end points. • Velocity = 20/1.2 = 17km/h

16. What is happening here?

17. What is happening here?

19. More Graphs • I initially said there were 3 cases (no slope, positive slope, negative slope). However, if we combine the type of velocity with the object’s position in relationship to the reference point, we can describe even more scenarios.

20. 1) On one graph draw the following: • an object that is stationary and behind the starting line. • an object that is stationary and in front of the starting line. • an object that is stationary and at the starting line. • 2) On one graph draw the following: • an object that is moving in a positive direction and starts behind the starting line. • an object that is moving in a positive direction and starts at the starting line. • an object that is moving in a positive direction and starts in front of the starting line. • an object that is moving in a positive direction but faster than the first object (starting at the starting line) • an object that is moving in a positive direction but slower than the first object (starting in front of the starting line) • 3) On one graph draw the following: • an object that is moving in a negative direction and starts behind the starting line. • an object that is moving in a negative direction but faster than the first object and starts at the starting line. • an object that is moving in a negative direction but slower than the first object and starts in front of the starting line.

21. Velocities • Ex. A player is on the +20. m line and runs 10 m/s. • Where will the player end up?

22. How can we use d-t graphs to determine v-t graphs? • Find the velocity for each section of the graph and plot it (make a list)

24. Starter: • Sketch a position-time graph of each object listed below. Describe its slope as positive or negative, and as constant, increasing, or decreasing. • A) a stone at rest • B) a jogger moving steadily to the right • C) a bicycle moving to the left and slowing down • D) a rocket moving up at an increasing speed • E) a stone falling freely with increasing speed • F) a parachutist drifting down at a steady speed

25. Non-Uniform Motion • An object does not always move at a constant speed. • You may speed up or slow down. • Non-uniform motion, when graphed, appears as a curve not a straight line.

26. Instantaneous Velocity • When you are driving on the highway and you look down at your speedometer, you are traveling at + 55 km/h. At that instant in time, + 55 km/h is your instantaneous velocity. • For uniform motion, your instantaneous velocity is the same as you average velocity. • For non-uniform motion, your instantaneous velocity changes.

27. Finding Instantaneous Velocity from a Graph • To find instantaneous velocity on a position - time graph, draw a line that is tangent to the curve at that point. • The slope is the instantaneous velocity (take the two points on the tangent from each side of the point).

28. Instantaneous Velocity (Uniform Motion)

29. Instantaneous Velocity (Non-uniform Motion)

30. Page 57 • Page 57, question 4 • Page 58, question 5 • Worksheet