1. DISTANCE VS DISPLACEMENT SPEED VS VELOCITY

2. DISTANCE – scalar quantity DISPLACEMENT – vector quantity A car travels 50 km to the East and then 20 km to the West, the total distance traveled is 70 km, but your displacement is 30 km East. E

3. Representing Displacement Let x1 be position of object at time t1 Let x2 be position at time t2 Then displacement x = x2 – x1  Greek letter delta) means change If a person starts at x 1 = 40m and walks to the left until reaching x 2 = 10m what is the displacement? Answer:  x = x 2 – x 1 = 10m – 40m = -30m

4. Average Speed and Velocity Velocity is speed and direction Average speed = distance traveled ÷ time elapsed Average velocity = displacement ÷ time elapsed Not always equal Find average speed and velocity for a trip 60m North followed by 40m South in 10 seconds. Answers: 10 m/s; 2 m/s N

5. Velocity shows how fast an object is moving in a certain direction. Average velocity can be calculated by dividing TOTAL displacement over TOTAL time.. (Ex) A car moved 50 km in 2 hours. The average velocity is 25 km/h because

6. Example During a four second interval a runner’s position changes from x 1 = 50m to x 2 = 10m. What was the average velocity? v av =  x/  t = x 2 – x 1 = -40m/4s = -10 m/s v av =  x/  t = x 2 – x 1 = -40m/4s = -10 m/s What is the average speed in kph? -10 m/s x 1 km/1000m x 3600 sec/ 1h = -36 km/h

7. INSTANTANEOUS VELOCITY Velocity at a particular instant of time. Defined as average velocity over an infinitesimally short time interval

8. INSTANTANEOUS VELOCITY The instantaneous velocity shows the velocity of an object at one point. For example, the speedometer of a car traveling along the autobahn (German freeway) swings to 200 km/h, indicates that the instantaneous velocity of the car is 200 km/h.

9. QUESTION: A car moved 20 km East and 60 km West in 2 hours. What is its average velocity in kph ? V ave = total displacement total time = 20 km – 60 km 2 h = - 20 kph or 20 kph W (negative indicates western direction)

10. QUESTION: How far (in km) will a car travel in 15 min at 20 m/s ? d = v t = (20 m) (60 s)(15 min) s min = 18 000 m = 18 km

11. Distance with constant velocity How far could a runner traveling at an average speed of 36 km/h go in 20 minutes? 20 min = 1/3 hour D x = v av  t = 36 km/h x 1/3h = 12 km = 1.2 x 10 4 m

12. Position-time graph simply shows the relationship between time and position. From the following data, for example, time (s)0 12345 position (m) 020 50130150 200 You can draw the following graph The tangent of a position- time graph represents velocity since

13. A velocity-time graph shows the relationship between velocity and time. For example, if a car moves at constant velocity of 5 m/s for 10 seconds, you can draw a velocity-time graph that looks like this: The area below the line represents the displacement the object traveled since it can be calculated by xy, or (time X velocity) which equals to displacement.