Some Motion Terms. Distance & Displacement Velocity & Speed Acceleration Uniform motion Scalar.vs. vector

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1 Motion

2 Some Motion Terms Distance & Displacement Velocity & Speed Acceleration Uniform motion Scalar.vs. vector

3 Scalar versus Vector Scalar - magnitude only (e.g. volume, mass, time) Vector - magnitude & direction (e.g. weight, velocity, acceleration)

4 Pictorial Representation An arrow represents a vector Length = magnitude of vector Direction = direction of vector

5 Pictorial Representation This arrow could represent a vector of magnitude 10 point to the right This arrow could represent a vector of magnitude 5 point to the left

6 Distance & Displacement Distance is the actual distance traveled. Displacement depends only on Start & Finish line Displacement is the distance traveled, in a certain direction.

7 Displacement Isn t Distance The displacement of an object is not the same as the distance it travels Example: Throw a ball straight up and then catch it at the same point you released it The distance is twice the height The displacement is zero

8 Distance & Displacement

9 Distance & Displacement B 4 m C 3 m 5 m A You walk from A to B to C. Your distance traveled is 7m Your displacement form A is 5 m

10 Velocity & Speed Velocity is the displacement traveled in a certain time. Speed is the distance traveled in a certain time. Velocity is speed in a given direction.

11 Types of Speed Instantaneous Speed is the speed at any specific instance Average Speed is the total distance covered divided by total time

12 Speed The average speed of an object is defined as the total distance traveled divided by the total time elapsed Average speed Speed d t Speed is a scalar quantity total distance total time

13 Velocity The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed Average velocity Velocity is a vector quantity total displacement total time V x t

14 Speed, cont Average speed totally ignores any variations in the object s actual motion during the trip The total distance and the total time are all that is important SI units are m/s

15 Velocity It takes time for an object to undergo a displacement The average velocity is rate at which the displacement occurs V average x t x f x i t f t i x f x i t generally use a time interval, so let t i = 0

16 Velocity continued Direction will be the same as the direction of the displacement (time interval is always positive) + or - is sufficient Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.) Other units may be given in a problem, but generally will need to be converted to these

17 Speed vs. Velocity Cars on both paths have the same average velocity since they had the same displacement in the same time interval The car on the blue path will have a greater average speed since the distance it traveled is larger

18 Speed vs. Velocity You drive from Yakima to Seattle (140 miles away) You stop in Ellensburg for a 2 hr lunch with a friend. Your total driving time is 2 hours Average speed Average speed 140 miles 2 hour 2 hour 140 miles 35 mph 4 hours

19 Uniform Velocity Uniform velocity is constant velocity The instantaneous velocities are always the same All the instantaneous velocities will also equal the average velocity

20 Velocity Example 150 Km/hr 100 Km/hr 50 Km/hr

21 Velocity again How fast is the plane moving in respect to the ground? Wind 35 Km/hr 100 Km/hr

22 Velocity, yet again How fast is the plane moving in respect to the ground? Wind 35 Km/hr 100 Km/hr

23 Velocity (finally) How fast is the plane moving in respect to the ground? Wind 35 Km/hr 100 Km/hr Result 65 Km/hr

24 Velocity again (??) How fast is the plane moving in respect to the ground? 100 Km/hr Wind 50 Km/hr

25 Velocity - the last time a 2 + b 2 = c Km/hr Resultant c 2 b 2 Wind 50 Km/hr a 2 How fast is the plane moving in respect to the ground?

26 (Last) Velocity How fast is the plane moving in respect to the ground? a 2 + b 2 = c Km/hr Resultant c 2 b 2 Wind 50 Km/hr R 2 = (100) 2 + (50) 2 R 2 = 10, R 2 = 12,500 R = Km/hr a 2

27 Acceleration Change in velocity divided by the change in time a V t

28 Acceleration Changing velocity (non-uniform) means an acceleration is present Acceleration is the rate of change of the velocity Units are m/s 2 (SI), cm/s 2 (cgs), and ft/s 2 (US Cust)

29 Average Acceleration Vector quantity When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

30 Instantaneous & Uniform Acceleration The limit of the average acceleration as the time interval goes to zero When the instantaneous accelerations are always the same, the acceleration will be uniform The instantaneous accelerations will all be equal to the average acceleration

31 Relationship Between Acceleration & Velocity Uniform velocity (shown by red arrows maintaining the same size) Acceleration equals zero

32 Relationship Between Velocity & Acceleration Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing (red arrows are getting longer) Positive velocity and positive acceleration

33 Relationship Between Velocity & Acceleration Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting shorter) Velocity is positive and acceleration is negative

34 Kinematic Equations Used in situations with uniform acceleration V f V 0 at V f 2 V 0 2 2a x x x 0 V 0 t 1 2 at 2

35 Kinematic Equations - Ex #1 A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 seconds. What is the car s final velocity?

36 Kinematic Equations - Ex #1 - Ans A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 seconds. What is the car s final velocity? V f V 0 at V f 6 m s 2 m s 2 6s 18 m s

37 Kinematic Equations - Ex #2 A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 meters. What is the car s final velocity?

38 Kinematic Equations - Ex #2 - Ans A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 meters. What is the car s final velocity? V f 2 V 0 2 2a x V 2 f 6 m s 2 V f 2 36 m2 s 2 V f 60 m2 s m s 2 6m m2 24 s m s m2 60 s 2

39 Kinematic Equations - Ex #3 A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 sec. How far does the car travel?

40 Kinematic Equations - Ex #3 - Ans A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s 2, for 6 sec. How far does the car travel? x x o V 0 t 1 2 at 2 x 0 6 m s 6s m s 6s 2 2 x 0 36m 36m 72m

Galileo Galilei 1564-1642 Galileo formulated the laws that govern the motion of

41 Galileo Galilei Galileo formulated the laws that govern the motion of objects in free fall Also looked at: Inclined planes Relative motion Thermometers Pendulum

42 Free Fall All objects moving under the influence of gravity only are said to be in free fall Free fall does not depend on the object s original motion All objects falling near the earth s surface fall with a constant acceleration The acceleration is called the acceleration due to gravity, and indicated by g

43 Acceleration due to Gravity Symbolized by g g = 9.81 m/s 2 g is always directed downward toward the center of the earth Ignoring air resistance and assuming g doesn t vary with altitude over short vertical distances, free fall is constantly accelerated motion

44 Free Fall an object dropped Initial velocity is zero Let up be positive Use the kinematic equations Generally use y instead of x since vertical Acceleration is g = m/s 2 v o = 0 a = g

45 Free Fall an object thrown downward a = g = m/s 2 Initial velocity 0 With upward being positive, initial velocity will be negative v o 0 a = g

46 Free Fall - example If a rock is dropped from a 18 building, and it takes seconds to reach the ground, how tall is the building?

47 Free Fall - answer What do we know? V 0 0 m s V f?? x?? a 9.81 m s 2 t 18sec

48 Free Fall - answer x(t) x 0 V 0 t 1 2 at2 x(t) (-9.81 m )(18 sec)2 2 s x(t) meters miles

49 Motion The End

HW Chapter 3 Q 14,15 P 2,7,812,18,24,25. Chapter 3. Motion in the Universe. Dr. Armen Kocharian

HW Chapter 3 Q 14,15 P 2,7,812,18,24,25 Chapter 3 Motion in the Universe Dr. Armen Kocharian Predictability The universe is predictable and quantifiable Motion of planets and stars description of motion