Exploring Motion: Understanding Speed and Velocity

2. Table of Contents 18 Chapter: Motion and Momentum Section 1: What is Motion? Section 2: Acceleration Section 3: Momentum

3. What is Motion? 1 Matter and Motion • All matter in the universe is constantly in motion, from the revolution of Earth around the Sun to elections moving around the nucleus of an atom.

4. What is Motion? 1 Changing Position • Something is in motion if it is changing position. • It could be a fast-moving airplane, a leaf swirling in the wind, or water tricking from a hose. • When an object moves from one location to another, it is changing position.

5. What is Motion? 1 Changing Position • The runners sprint from the start line to the finish line. • Their positions change, so they are in motion.

6. What is Motion? 1 Relative Motion • An object changes position if it moves relative to a reference point. • Picture yourself competing in a 100-m dash. • You begin just behind the start line. • When you pass the finish line, you are 100 m from start line.

7. What is Motion? 1 Relative Motion • If the start line is your reference point, then your position has changed by 100 m relative to the start line, and motion has occurred.

8. What is Motion? 1 Distance and Displacement • Displacement includes the distance between the starting and ending points and the direction in which you travel. • This figure shows the difference between distance and displacement.

9. What is Motion? 1 Speed • Speed is the distance traveled divided by the time taken to travel the distance. • Speed can be calculated from this equation:

10. What is Motion? 1 Speed • In SI units, distance is measured in m and time is measured in s. • As a result, the SI unit of speed is the m/s—the SI distance unit divided by the SI time unit.

11. What is Motion? 1 Average Speed • Average speed is found by dividing the total distance traveled by the time taken. • An object in motion can change speeds many times as it speeds up or slows down.

12. What is Motion? 1 Average Speed • The speed of an object at one instant of time is the object's instantaneous speed. • If it takes you 0.5 h to walk 2 km to the library, your average speed would be as follows:

13. What is Motion? 1 Average Speed • Average speed, instantaneous speed, and constant speed are illustrated here.

14. What is Motion? 1 Graphing Motion • You can represent the motion of an object with a distance-time graph. • For this type of graph, time is plotted on the horizontal axis, and distance is plotted on the vertical axis. Click box to view movie.

15. What is Motion? 1 Distance-Time Graphs and Speed • Look at the graph. • According to the graph, after 1 s student A traveled 1 m. • Student B, however, traveled only 0.5 m in the first second.

16. What is Motion? 1 Distance-Time Graphs and Speed • So student A traveled faster than student B. • The line representing the motion of student A is steeper than the line for student B.

17. What is Motion? 1 Distance-Time Graphs and Speed • A steeper line on the distance-time graph represents a greater speed. • A horizontal line on the distance-time graph means that no change in position occurs.

18. What is Motion? 1 Velocity • If you are hiking in the woods, you want to know not only your speed, but also the direction in which you are moving.

19. What is Motion? 1 Velocity • The velocity of an object is the speed of the object and direction of its motion. • This is why a compass and a map are useful to hikers.

20. What is Motion? 1 Velocity • Velocity has the same units as speed, but it also includes the direction of motion. • The velocity of an object can change if the object's speed changes, its direction of motion changes, or they both change.

21. Section Check 1 Question 1 To determine whether something has changed position, you need a _______. A. compass B. global positioning system C. map D. reference point

22. Section Check 1 Answer The answer is D. If someone starts a car and drives it 100 meters from its parking spot, the parking spot can be used as a point of reference to show that the car moved.

23. Section Check 1 Question 2 Displacement includes your _______ and _______ as well as the _______ in which you have traveled.

24. Section Check 1 Answer It includes your starting point, ending point, and direction in which you have traveled. It is possible to have traveled a great distance and still have a displacement of zero if you traveled in an enormous circle and ended right where you began.

25. Section Check 1 Question 3 Speed equals distance divided by _______. A. force B. mass C. time D. velocity

26. Section Check 1 Answer The answer is C. The smaller the t value in s=d/t, the greater the speed.

27. Acceleration 2 Acceleration and Motion • Accelerationis the change in velocity divided by the time it takes for the change to occur. • Acceleration has a direction. • If an object speeds up, the acceleration is in the direction that the object is moving.

28. Acceleration 2 Acceleration and Motion • If an object slows down, the acceleration is opposite to the direction that the object is moving. • If the direction of the acceleration is at an angle to the direction of motion, the direction of motion will turn toward the direction of the acceleration.

29. Acceleration 2 Speeding Up • When an object that is already in motion speeds up, it also is accelerating. • When the speed of an object increases, it is accelerating. • The toy car is accelerating to the right. Its speed is increasing.

30. Acceleration 2 Slowing Down • Acceleration occurs when an object slows down, as well as when it speeds up. • The car is slowing down. • During each time interval, the car travels a smaller distance, so its speed is decreasing.

31. Acceleration 2 Changing Direction • Motion is not always along a straight line. • If the acceleration is at an angle to the direction of motion, the object will turn. • At the same time, it might speed up, slow down, or not change speed at all.

32. Acceleration 2 Changing Direction • Motion is not always along a straight line. • If the acceleration is at an angle to the direction of motion, the object will turn. • At the same time, it might speed up, slow down, or not change speed at all. Click image to view movie.

33. Acceleration 2 Calculating Acceleration • If an object is moving in a straight line, its acceleration can be calculated using this equation. • In SI units, acceleration has units of meters per second squared (m/s2).

34. Acceleration • When you speed up, your final speed always will be greater than your initial speed. 2 Positive and Negative Acceleration • So subtracting your initial speed from your final speed gives a positive number. • As a result, your acceleration is positive when you are speeding up.

35. Acceleration 2 Positive and Negative Acceleration • When your final speed is less than your initial speed, your acceleration is negative. • Therefore, your acceleration is negative when you slow down.

36. Acceleration 2 Graphing Accelerated Motion • The motion of an object that is accelerating can be shown with a graph. • For this type of graph, speed is plotted on the vertical axis and time on the horizontal axis.

37. Acceleration 2 Graphing Accelerated Motion • An object that is speeding up will have a line on a speed-time graph that slopes upward. • An object that is slowing down will have a line on a speed-time graph that slopes downward. • A horizontal line on the speed-time graph represents an acceleration of zero or constant speed.

38. Section Check 2 Question 1 A change in velocity divided by the time it takes for the change to occur equals the object’s _______.

39. Section Check 2 Answer The answer is acceleration. Remember that, like velocity, acceleration has a direction. A car that takes a turn has changed its acceleration, even if nothing else changes.

40. Section Check 2 Question 2 Imagine yourself driving a car down an empty stretch of road. How many ways could you change your acceleration?

41. Section Check 2 Answer You could step on the gas; you could also step on the brake; you could turn the wheel, or do any combination of these.

42. Section Check 2 Question 3 What is happening at point C in this speed-time graph?

43. Section Check 2 A. the object is speeding up B. the object is slowing down C. the object is at rest D. the object is gone

44. Section Check 2 Answer The answer is B. When the line falls, the object is slowing down.

45. Momentum 3 Mass and Inertia • The mass of an object is the amount of matter in the object. • In SI units, the unit for mass is the kilogram. • The weight of an object is related to the object's mass.

46. Momentum 3 Mass and Inertia • Objects with more mass weigh more than objects with less mass. • However, the size of an object is not the same as the mass of the object.

47. Momentum 3 Mass and Inertia • The more mass an object has, the harder it is to start it moving, slow it down, speed it up, or turn it. • This tendency of an object to resist a change in its motion is calledinertia. • Objects with more mass have more inertia.

48. Momentum 3 Momentum • The momentum of an object is a measure of how hard it is to stop the object, and it depends on the object's mass and velocity. • Momentum is usually symbolized by p.

49. Momentum 3 Momentum • Mass is measured in kilograms and velocity has units of meters per second, so momentum has units of kilograms multiplied by meters per second (kg . m/s). • Momentum has a direction that is the same as the direction of the velocity.

50. Momentum 3 Conservation of Momentum • According to the law of conservationof momentum, the total momentum of objects that collide is the same before and after the collision. • This is true for the collisions of billiard balls, as well as for collisions of atoms, cars, football players, or any other matter.