Motion

1. Motion Speed, Velocity, and Acceleration

2. What is motion? • Motion is easy to recognize but can be hard to describe • Motion simply put is a change in position • The following quantities are used to describe motion: speed, velocity and acceleration • Each of these is a rate. A rate is a quantity divided by time.

3. Recap: Motion • Motion • Change in position during a time period • 3 types of motion • Speed • Velocity • Acceleration

4. So how is a difference in position determined? • First let us define distance • It is simply the linear space between two points • So from where do we begin our measurement? • From a point of reference

5. Point of Reference • Movement is relative to an object that appears to be stationary • This means that we describe motion of an object relative to some other object • The object or point from which movement is determined is called the point of reference • For us, the reference for motion is Earth or Earth’s surface, and speed and distance are measured relative to the earth

6. In Which Direction Does Motion Occur? • Motion can occur in many directions; this can be exhibited on a coordinate axis • We generally determine distance along the x-axis, and for our calculations we will use the x-axis • But there are 2 other axes on which motion occurs (we will address this later)

7. Now that we have determined direction, how do we decide what factors we will consider? • Sometimes when we make calculations we are not concerned with the direction; while other times direction becomes a very important factor that must be accounted for. • Because of this, dimensional (measurable) quantities have been separated into 2 categories… • Scalar Quantities • Vector Quantities

8. Characteristics of a Scalar Quantity • Only has magnitude(greatness of a measurement) • Requires 2 things: 1. A value (a number) 2. Appropriate units Ex. Mass: 5kg Temp: 21° C Speed: 65 mph

9. Characteristics of a Vector Quantity • Has magnitude & direction • Requires 3 things: 1. A value 2. Appropriate units 3. A direction! Ex. Acceleration: 9.81 m/s2 down Velocity: 25 mph West

10. Vector Quantities • The best way to remember this is that a vector must have magnitude and direction…. Oh Yeah!

11. Speed

12. Question • When can you determine how fast you are going in a jet plane?

13. Speed • Speed • 1. Definition: Rate at which an object moves • 2. Formula: Distance divided by time (d/t) • 3. Units: m/s or km/s

14. Distance vs. Time

15. Speed d s t • Speed is a measure of how fast something is moving. • It is the rate at which a distance is covered • Units of speed could be: km/h, m/s, mi/h, ft/s • In physics we use units of m/s for speed • Speed is a scalar quantity • s = d/t

16. Instantaneous Speed • Instantaneous speed is speed at any instant in time. • A speedometer measures speed in ‘real time’ (the instantaneous speed).

17. Average Speed Average speed is the average of all instantaneous speeds; found simply by a total distance/total time ratio The average speed of a trip:

18. Average speed • Total distance divided by the total time • Formula: • Total distance • total time

19. Speed: Average vs. Instantaneous

20. Calculating Speed: Example • If 2 runners ran the same distance (10km) but one completed it in 3600 seconds and the other in 2800 seconds, what were each of their average speeds? • 1: d/t 10.0 km/3600. sec 0 .00278 km/sec • 2: d/t 10.0 km/ 2800. sec 0 .00357 km/sec • Runner 2 has greatest average speed!

21. Calculating Speed: Example • Spirit of Australia, a hydroplane boat, made speed records by traveling 239 miles in 0.75 hours (45 minutes). What is it’s record breaking speed? • d/t 239 miles/ 0.75 hr 318.7 mph or ~320 mph

22. Velocity

23. Velocity • Speed in a given direction • Velocities in the same direction combine by adding • Velocities in different directions combine by subtracting

24. Velocity Triangle d v t • Speed and velocity triangles are similar because v = d/t • Find the equation for displacement, and time using the triangle • d = v x t • t = d/v

25. Velocity • Velocity • 1. Definition: Rate at which an object moves in a given direction • 2. Formula: Displacement divided by time (d/t) • 3. Units: m/s, km/s.km/hr, mph • And direction: North, South, East or West

26. Calculating Velocity: Example • If a runner is running east at 10 m/s sec, what is her velocity? • 10 m/s east

27. Calculating Velocity: Example • If you’re rowing a boat downstream at 16 km/hr, and the current is moving at 10.0 km/hr. How fast does the boat “look” like it’s going to someone on shore? (Draw a picture too!) • 16 km/hr + 10.0 km/hr • 26 km/hr downstream

28. Calculating Velocity: Example • If you’re rowing a boat upstream at 15 km/hr, against a current moving at 8 km/hr. What is you’re actual velocity to an observer on the shore? • 15 km/hr - 8 km/hr • 7 km/hr upstream

29. Calculating Velocity: Example • If you are running up an escalator at 2 steps per second and its moving downward at 3 steps per second, what is the total velocity? In what way are you moving? • -3 steps/s + 2 steps/s • -1 step/s • (you are actually moving backwards, down the escalator, although you’re running up it)

30. Velocity Questions 30 m Speed up, Slow down, turn NO They do not have the same velocity because they are travelling in different directions! How far does Bob run if he maintains an average velocity of 3 m/s for 10 s? List three ways you can change the velocity of your car. Is it possible to go around a corner without changing velocity? Explain. One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain.

31. Velocity • Velocity • Velocities can be combined • Add velocities when in same direction • Velocities in opposite direction= subtract

32. More about Vectors • We represent a vector by drawing an arrow • 1. the length represents magnitude • 2. the arrow faces the direction of motion • When we add or subtract vectors the result is called the resultant

33. Mathematical Addition of Vectors • Vectors in the same direction: Add the 2 magnitudes, keep the direction the same. Ex. + = 3m E 1m E 4m E

34. Mathematical Addition of Vectors • Vectors in opposite directions Subtract the 2 magnitudes, direction is the same as the greater vector. Ex. 4m S + 2m N = 2m S

35. Mathematical Addition of Vectors • When vectors meet at 90° • The resultant vector will be hypotenuse of a right triangle. • Use the Pythagorean Theorem to find the resultant. a2 + b2 = c2

36. Vectors at a right angle 30 km/hr 40 km/hr • Determine your resultant velocity if you are traveling in a boat 40 km/hr North and the river’s current is moving 30 km/hr East. • a2 + b2 = c2 • (40 km/hr)2 + (30 km/hr)2 = c2 • 1600 km2/hr2 + 900 km2/hr2 = c2 • 2500 km2/hr2 = c2 • √ 2500 km2/hr2 = √c2 • C= 50 km/hr

37. Questions • How is velocity different from speed? • Which two factors determine an object’s velocity?

38. Velocity and Speed • In physics we distinguish between speed and velocity: • Speedrefers to how quickly an object moves (a scalar quantity). • Velocityis defined as speed in a given direction or rate of change of position (displacement over time). v = x/t • Velocity refers to both the speed and directionof motion of an object (a vector quantity). • Negative velocity means the object is moving in the opposite direction • Motion at constant velocity means that both the speed and direction of an object do not change. • In a car, we can change the velocity three ways: gas pedal to speed up, brake to slow down or steering wheel to change direction

39. Acceleration

40. Acceleration • Acceleration • 1. Definition: Rate of change in velocity • Speeding up, slowing down, changing direction • 2. Formula: Final velocity minus original velocity, divided by time • 3. Units: m/s/s or km/s/s

41. Acceleration • 4. Increasing velocity - positive acceleration • 5. Decreasing velocity - negative acceleration- deceleration

42. Acceleration • The change in velocity • Acceleration is measured in m/sec/sec or m/sec2 • Formula is: • (final velocity – initial velocity) time

43. Velocity vs. Time

44. Acceleration • For its velocity to change, an object must accelerate. • An object accelerates whenever its speed or direction or both change. • Acceleration may be positive (increasing speed) or negative (decreasing speed). • Accelerationis a measure of how quickly the velocity changes: a = Dv/t

45. Acceleration at constant speed • An object moving in a circle at constant speed is always accelerating (changing direction).

46. Solving Acceleration Problems using Acceleration Triangle Dv a t • If you have starting and ending velocity or speed, find that before you use the triangle. • If not, use triangle to find change in velocity (Dv), then find initial or final velocity • Dv = final velocity – initial velocity

47. Deceleration vs. Acceleration • A decrease in velocity is deceleration or negative acceleration • An increase in velocity is a positive acceleration

48. Change in Velocity • Each time you take a step you are changing the velocity of your body. • You are probably most familiar with the velocity changes of a moving bus or car. • The rate at which velocity (speed or direction) changes occur is called acceleration.

49. Acceleration= final velocity- initial velocity time Change in velocity = final – initial velocity velocity Acceleration= change in velocity time

50. A car traveling at 60. mph accelerates to 90. mph in 3.0 seconds. What is the car’s acceleration? Velocity(final) - Velocity(initial) = Acceleration time 90. mph – 60. mph = 0.00083 hours 30 mph = 0.00083 hours = 36000 mph2