Motion

2. Objectives Identify frames of reference and describe how they are used to measure motion Identify appropriate SI units for measuring distances Distinguish between distance and displacement Calculate displacement using vector addition

3. Choosing a Frame of Reference Definition - system of objects that are not moving with respect to one another How fast are you moving? - depends on relative motion; movement in relation to a frame of reference ex. person riding a bike - to a person walking or standing still on the sidewalk the bike is speeding by - to a person in a car the bike is moving slowly

4. Frame of Reference Cont. Which frame should you choose? - needs to be meaningful to describe motion clearly ex. want to know the speed of the biker - would not use on object moving with or besides the bike: a person walking - WOULD use a object not moving and not located on the bike: a tree

5. Measuring Distance Definition - length of the path between two points ex. your house and the movie theater - base unit: meters (m) - kilometers (km): for large distances ex. length of the salt river - centimeters (cm): for small distances ex. distance a marble rolls

6. Measuring Displacement Definition - direction from the starting point and the length of a straight line from the starting point to the ending point - often used in when giving directions - needs to be precise and accurate ex. walk 3 blocks east from the train depot - possible to be “zero”, move but end up in the same location you started

7. Measuring Displacements Cont. Combining displacements - use vectors, a quantity that has magnitude and direction magnitude: size, length, or amount directions: single or multiple: N or NW - Straight Line Displacements: add or subtract add: vectors are in the same directions ex. 5 km W + 7 km W = 12 km W subtract: vectors are opposite ex.15 km N – 3 km S = 12 km N

8. Measuring Displacements Cont. - Non-straight Line Displacements: Graph - find the resultant vector: sum of two or more vectors ex. - distance is 9 blks - displacement is about 7.3 blks

9. Speed Definition - ratio of distance an object moves to the amount of time the object moves Formula - Speed = Distance/Time Types - average: total distance over total time ex. car trip to California you may have reached speed between 5 mph and 85 mph averaging 62 mph - instantaneous: measured at any given moment ex. cop using a radar gun as you pass

10. Speed Problems Calculate and Solve a.) A runner completes a 10.0 km race in exactly 30 minutes. At 2 km his speed was marked at 2 km/m. 20 minutes later his speed was marked at 1.7 km/m What is the runner’s average speed? What is the runner’s instantaneous speed 2 km into the race? Average speed = total distance = 10.0km = .33km/min total time 30 min Instantaneous speed = 2km/m

11. Velocity Definition - speed and direction in which an object is moving Formula - Velocity = distance + direction time Combining Velocity - Velocity Vectors Parallel opposite direction: subtract same direction: add

12. Velocity Vectors ex. airplane flying due N at 100 km, with a tail wind due N at 20 km: * note 1 cm = 20 km/h 120 km/h with tail wind 100 km/h without tail wind Non Parallel Vectors - Resultant: algebraic sum of two or more vectors ex.

13. Velocity Vectors Cont. Parallelogram Rule - construct a parallelogram with two vectors as adjacent sides, tails together - diagonal is the resultant ex. - find the sum of the resultant use Pythagorean’s theorem (must have a right angle) - a2 + b2 = c2

14. Velocity Vector Problems a.) A bird flies south for the winter at an average speed of 5km/m, facing a north wind of 1km/m. Draw velocity vectors and calculate the birds velocity? b.) The birds returns north in the summer under the same conditions. Draw velocity vectors and calculate the birds velocity? c.) A bird flies south for the winter at an average speed of 4km/m, under extremely stormy conditions the wind is due east at 2km/m. What is the birds velocity

15. Velocity Vectors Problems Answers a.) 4km/m S b.) 1 km/m N 6km/m N 5 km/m N c.) 4.5 km/m SE

16. Apply the Concepts of Speed & Velocity Can the terms speed and velocity be used interchangeably? Yes, only when direction is not of importance ex. If you have a constant speed do you have a constant velocity? Not necessarily ex.

17. Acceleration Definition - rate at which velocity changes - speed, direction or both can change - can be + (increasing) or - (decreasing) Formula - Vf- Vi t

18. Practice Problems A car traveling at 10m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is it’s acceleration? A: A = Vf – Vi/t (0m/s – 10m/s)/20m/s = -0.5m/s2 An airplane travels down a runway for 4.0 s with an acceleration of 9.0m/s2 . What is it’s change in velocity during this time? A: (Vf – Vi) = at (9.0m/s2) (4.0s) = 36m/s

19. Graphing Speed/Velocity Distant Time Graph - relationship between speed, distance and time - use the formula for speed: D/t - speed can be found by calculating the slope of the line distance (m) time (s) - constant speed will have a slope of 0 * moving but not accelerating* distance ex. car moving at 5 m/s (m) *velocity must include a direction time (s)

20. Graphing Acceleration Graphing - velocity time graph - velocity on vertical axis - time on horizontal axis positive slope: speed increasing negative slope: speed is decreasing straight line: constant speed