Kinematics Chapter 3: LINEAR MOTION

1. Kinematics Chapter 3: LINEAR MOTION • http://highered.mcgraw-hill.com/sites/0070524076/student_view0/interactives.html • straight-line path—linear motion • http://www.mhhe.com/physsci/physical/giambattista/forces/forces.htm • http://www.mhhe.com/physsci/physical/giambattista/forces/forces.htm

2. Chapter 3: LINEAR MOTION Chelcie Liu asks his students to check their neighbors and predict which ball will reach the end of the equal-length tracks first.

3. Chapter 3: LINEAR MOTION The rules of motion involve three concepts: Speed Velocity acceleration Become familiar with them and be able to distinguish between them. Here we'll consider only the simplest form of motion—that along a straight-line path—linear motion.

4. Motion Is Relative • Everything moves. • Even things that appear at rest move. They move relative to the sun and stars. • You're moving at about 107,000 km/hr relative to the sun. And even faster relative to the center of our galaxy. • When we discuss the motion of something, we describe motion relative to something else.

5. Motion Is Relative • When walking down the aisle of a moving bus, your speed is relative to the floor of the bus – which is likely quite different from your speed relative to the road. • a racing car with a speed of 300 km/hr is relative to the track. • Unless stated otherwise, when we discuss the speeds of things in our environment we mean relative to the surface of the Earth.

6. Scalar Quantities • Scalars are quantities which are fully described by a magnitude alone. • Examples of scalar quantities are distance, speed, mass, volume, temperature, density and energy.

7. Force and Motion • Linear MotionLinear motion is the movement of an object along a straight line.

8. Distance vs Displacement Distance Displacement the shortest distance of the object from point O in a specific direction.Unit: metre (m)Type of Quantity: Vector quantity The total length that is traveled by that object.Unit: metre (m)Type of Quantity: Scalar quantity

9. Displacement = 120 m, in the direction of Northeast Displacement is a vector quantity • Distance traveled = • 200 m • Distance is a scalar quantity

10. VectorQuantities • Vectors are quantities which are fully described by both a magnitude and a direction. • Examples of vector quantities are displacement, velocity, acceleration, force,

11. Speed is the rate of change in distance. • Type of quantity: Scalar quantity

12. Speed • Speed is a measure of how fast something moves, measured by a unit of distance divided by a unit of time • Any combination of distance and time units is legitimate for measuring speed; • for motor vehicles (or long distances) the units kilometers per hour (km/h) or miles per hour (mi/h or mph) are commonly used. • shorter distances, meters per second (m/s) are often useful units.

13. Approximate Speeds in Different Units

14. Velocity is the rate of change in displacement • Vector quantity

15. Instantaneous Speed • Cars vary in speed on a trip • You can tell the speed of the car at any instant by looking at its speedometer. • The speed at any instant is the instantaneous speed.

16. Average Speed • Average speed is defined as: • the whole distance covered divided by the total time of travel • it doesn't indicate the different speeds and variations that may have taken place during shorter time intervals.

17. Check Yourself 1. What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s?2. If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km.(a) How far would it travel if it moved at this rate for 4 h? (b) For 10 h? 3. In addition to the speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one-half hour later, what has been your average speed?4. Would it be possible to attain this average speed and never go faster than 80 km/h?

18. Velocity • Speed = distance / time • Velocity = distance/time + direction • The car on the circular track may have a constant speed, but its velocity is changing every instant. Why?

19. Velocity • We distinguish between average velocity and instantaneous velocity as we do for speed • Velocity alone is assumed to mean instantaneous velocity

20. Velocity • If something moves at an unchanging or constant velocity, then, its average and instantaneous velocities will have the same value. • The same is true for speed

21. Velocity • Constant velocity means constant speed with no change in direction. . • A car that rounds a curve at a constant speed does not have a constant velocity—its velocity changes as its direction changes.

22. Velocity • Constant velocity and constant speed, however, can be very different • Constant velocity means constant speed with no change in direction. • A car that rounds a curve at a constant speed does not have a constant velocity—its velocity changes as its direction changes

23. Constant velocity means constant speed with no change in direction. • A car that rounds a curve at a constant speed does not have a constant velocity—its velocity changes as its direction changes.

24. The best way to imagine a situation with several physical quantities is by drawing a graph. • To picture the behaviorof the speed of an object, we plot the distance on the vertical axis and the time on the horizontal axis.

25. Here, the total distance travelled ( y) divided by the time taken ( x) is the gradient of the slope. This is also equal to the average speed of the object - remembering that In this case, the speed is constant as the slope of the distance-time graph is constant.

26. By re-arranging the equation we can plot slopes of either distance, or time, on a graph to find their values. For example, we can see how to find the distance from a speed-time graph by rearranging to get: • We then plot a speed-time graph as shown below: The blue rectangle has an area equal to the speed multiplied by the time. We can see from the equation above, that this is equal to the distance travelled.

27. The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

28. During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?

29. Acceleration • We can change the velocity of something by changing its speed, by changing its direction, or by changing both its speed and its direction.

30. Acceleration on Galileo's Inclined Planes • Galileo lacked suitable timing devices to fime falling objects • he used inclined planes to slow down accelerated motion and investigate it more carefully.Galileo found that a ball rolling down an inclined plane will pick up the same amount of speed in successive seconds; that is, the ball will roll with unchanging acceleration.

31. Acceleration on Galileo's Inclined Planes • a ball rolling down a plane inclined at a certain angle might be found to pick up a speed of 2 meters per second for each second it rolls. This gain per second is its acceleration. Its instantaneous velocity at 1-second intervals, at this acceleration, is then 0, 2, 4, 6, 8, 10, and so forth meters per second

32. Galileo found greater accelerations for steeper inclines. • The ball attains its maximum acceleration when the incline is tipped vertically. Then the acceleration is the same as that of a falling object

33. Free FallTable 3.2 shows the instantaneous speed of a freely falling object at 1-second intervals

34. Free Fall • During each second of fall, the object gains a speed of 10 meters per second. • Free-fall acceleration is approximately equal to 10 m/s2

35. freely falling objects use g because the acceleration is due to gravity • g varies slightly in different locations, dependent on mass • Where accuracy is important, the value of 9.8 m/s2 should be used.

36. Free Fall • When a falling object is free of all restraints—no friction, air or otherwise, and falls under the influence of gravity alone, the object is in a state of free fall.

37. The instantaneous velocity of an object falling from rest can be expressed in shorthand notation as V = gt • the instantaneous velocity or speed in meters per second is simply the acceleration g = 10 m/s2 multiplied by the time t in seconds.

38. a falling rock is equipped with a speedometer. • In each succeeding second of fall, you'd find the rock's speed increasing by the same amount: 10 m/s.

39. How about an object thrown straight upward? • Once released, it continues to move upward for a while and then comes back down. • At the highest point, when it is changing its direction of motion from upward to downward, its instantaneous speed is zero. • Then it starts downward just as if it had been dropped from rest at that height.

40. How about an object thrown straight upward? • the object slows as it rises. at the rate of 10 meters per second each second—the same acceleration it experiences on the way down. • the instantaneous speed at points of equal elevation in the path is the same whether the object is moving upward or downward • The velocities are opposite, because they are in opposite directions. • the downward velocities have a negative sign, indicating the downward direction

41. How about an object thrown straight upward? • Whether moving upward or downward, the acceleration is 10 m/s2 the whole time. • up positive, and down negative.

44. Air Resistance • is responsible for different accelerations • a feather and a coin in the presence of air fall with different accelerations. • But in a vacuum, the feather and coin fall with the same acceleration

45. Acceleration • it is a rate of a rate • Acceleration is not velocity, nor is it even a change in velocity. Acceleration is the rate at which velocity itself changes

47. vertical motion • The relationship between time up or down and vertical height is given by

48. We're talking here of vertical motion. • How about running jumps? Hang time depends only on the jumper's vertical speed at launch. While airborne, the jumper's horizontal speed remains constant while the vertical speed undergoes acceleration. Interesting physics!

49. Summary of Terms •   Speed How fast something moves. The distance traveled per unit of time.  Velocity The speed of an object and specification of its direction of motion.  Acceleration The rate at which velocity changes with time; the change in velocity may be in magnitude or direction or both.  Free fall Motion under the influence of gravity only.

50. Summary of Formulas • Speed = distance/time • Average speed = total distance covered • time interval • Acceleration = change of velocity • time interval • Acceleration (linear) = change in speed • time interval • Freefall velocity from rest v = gt • Distance fallen in freefall from rest