How Do We Describe Motion?

1. How Do We Describe Motion? • Motion in 1-D

2. Adding vectors To add vectors graphically they must be placed “tip to tail”.The result (F1 + F2) points from the tail of the first vector to thetipof the second vector. F1 F2 For collinear vectors: Fnet ? F1 F2 Fnet ?

3. Adding Vectors Lengthb Lengtha c Θb a a2+ b2= c2 Tan θ =b/a

4. Adding Vectors • Can also add • Same result as before

5. Components a=c cosθ b=c sinθ c b θ a2 +b2= c2 a

6. How fast is this plane moving? 200 100 Cross wind

8. Velocity Velocity is a vector that measures how fast and in what direction something moves. Δ is a symbol it is not a quantity Δr is the (vector) displacement Speed is the magnitude of the velocity. It is a scalar.

11. x (m) x2 x1 t2 t1 t (sec) More general motion, non uniform motion On a graph of position versus time, the average velocity is represented by the slope of a chord.

13. x (m) t (sec) This is represented by the slope of a line tangent to the curve on the graph of an object’s position versus time.

14. Slide 2-16

15. \ Motion diagram (student walking to school) Graph Table of data Slide 2-13

20. Checking Understanding A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? A. B. C. D. Slide 2-19

21. Answer A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? C. A. B. D. Slide 2-20

22. Checking Understanding Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? A. B. C. D. Slide 2-17

23. Answer Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? C. A. B. D. Slide 2-18

24. Velocity The velocity is a vector. It changes if we change • the speed • the direction i.e. driving around a curve even at constant speed.

25. Findingdwhen we know v Consider only x component Δx = vxΔt or xf = xi +vxΔt If vx = v1(constant) vxΔt is the same as the area in graph of v /t

26. If V is not constant we can still use area in graph

27. Example :Speedometer readings are obtained and graphed as a car comes to a stop along a straight-line path. How far does the car move between t = 0 and t = 16 seconds? Since there is not a reversal of direction, the area between the curve and the time axis will represent the distance traveled.

29. Example Problem A soccer player is 15 m from her opponent’s goal. She kicks the ball hard; after 0.50 s, it flies past a defender who stands 5 m away, and continues toward the goal. How much time does the goalie have to move into position to block the kick from the moment the ball leaves the kicker’s foot? Slide 2-25

31. acceleration Acceleration is a vector (since v is a vector)

33. Which has a greater acceleration an airplane going from 1000 km/hr to 1005 km/hr in 5 seconds or a skateboarder going from 0 to 5 km/hr in 1 second? • The airplane • The skateboarder

34. Acceleration • Acceleration is: • The rate of change of velocity • The slope of a velocity-versus-time graph Slide 2-26