2. Position & Distance & Average Velocity  Objectives:  Ch. 2 p. 19 - 23  Define kinematics  Know what a reference frame is  Define the terms position, displacement, average velocity  To used v ave = Δd/Δt to solve simple kinematic problems  (Note Your text book uses x in place of d for distance.)

3. Position & Distance I want to give you a brand new “Ferrari Testarossa”. It is worth about $250000. All you have to do is go and pick it up. It is 5.0 km away. What is the problem with this?

4. Position & Distance Before we can describe how something moves we need to discuss where it is and how to find it at a new location. 0123456789101112-4-3-2 AB What is the position of car A relative to car B? The position of the cars can now be accurately stated To answer this we need some sort of reference point and some frame of reference to measure the position of the two cars. Reference point Reference frame

5. Position & Distance Car A is at Position: -1 m 0123456789101112 m-4-3-2 AB Distance is the separation between the two cars and does not need any reference frame Therefore the distance between car A and Car B is 11 m Car B is at Position: 10 m Separation

6. Average Velocity Let us discuss a situation in which a single car is moving with respect to a stationary reference frame (the ground for example). 0102030405060708090100110120 m-40-30-20-10 Clock Readings (s) Position (m) 0.00 2.020 4.080 6.0120 The car’s position was determined as a function of time. The data table on the right shows this. t = 0t = 4.0t = 6.0t = 2.0

7. Average Velocity To determine the average velocity or speed of the car we need to know it’s change in position and the time required for this change. Change in position (called displacement or Δd) is the distance the car travels during a defined time period. 0102030405060708090100110120 m-40-30-20-10 t = 2.0t = 4.0 Δd = d 2 – d 1 =80 – 20 = 60 m Δt = t 2 – t 1 =4.0 – 2.0 = 2.0 s Note: Your text book uses x 2 and x 1 to represent positions.

8. Average Velocity average velocity = Time displacement v ave = ΔdΔd ΔtΔt d 2 – d 1 t 2 – t 1 = v ave = 80 – 20 4.0 – 2.0 = 60 m 2.0 s v ave = 30 m/s From the pervious slide:

9. Average Velocity What was the car’s average velocity between: Clock Readings (s) Position (m) 0.00 2.020 4.080 6.0120 1) t = 0 and t = 4.0 ? 2) t = 2.0 and t = 6.0 ? 3) t = 4.0 and t = 6.0 ? v ave = 80 – 0 4.0 – 0.0 = 20 m/s v ave = 120 – 20 6.0 – 2.0 = 25 m/s v ave = 120 – 80 6.0 – 4.0 = 20 m/s Did the car travel at a constant velocity during it’s trip? How do you know this?

10. Average Velocity Battle of the units: Two units for velocity can be used in this course. One you have ready seen (m/s) The other is one that is commonly used by everyone: kilometers per hour (km/h). Posted on streets signs is the maximum speed in km/h:

11. Average Velocity What does 55 km/h mean? Ans: If a vehicle travels at this speed it will cover 55 km in one hour. In physics we prefer to use m/s. We can convert between the two using a very simple formula: m/s km/h X 3.6 ÷ 3.6

12. Average Velocity Now try These: Fill in the missing velocity ObjectVelocity (m/s)Velocity (km/h) Car55 Plane120 Person walking5.0 Space Shuttle7100 Earth in orbit about the sun 9.72 x 10 7 15 430 1.4 26000 2.7 x 10 7

13. Average Velocity Example problems: 1. A car travels a distance of 440 m in a time of 7.20 s. What was it’s average velocity ? v ave = 440 m 7.20 s = 61 m/s v ave = ΔdΔd ΔtΔt (or 220 km/h) Show the formula!! Show the substitution!! Answer in correct number of sig. Figs and has correct units

14. Average Velocity Example problems: 2. A plane travels at 230 km/h for a time of 6.5 h. How far did it travel (what is it’s displacement)? Δd = 230 km/h x 6.5 h = 1500 km Δd = v ave X Δt Re-arrange the equation Show the substitution!! Answer in correct number of sig. Figs and has correct units

15. Average Velocity Example problems: 3. An ant covers a distance of 2.6 m while travelling at an average velocity of 0.14 m/s. How much time is required for the ant’s journey? Δt = 2.6 m 0.14 m/s = 19 s v ave ΔdΔd Δt = Re-arrange the equation Show the substitution!! Answer in correct number of sig. Figs and has correct units

16. Average Velocity 1) Complete Speed Worksheet. 2) Problems #1 – 3, 5 – 7, 9 & 12 p. 39 of your text book. Time to practice so you will understand these concepts:

17. Position & Distance