1. Chapter 2 Motion in ONE dimension

2. Displacement This chapter we are only doing to study motion in one direction. This chapter we are only doing to study motion in one direction. Motion takes place over time and depends on frame of reference. Motion takes place over time and depends on frame of reference. Frame of Reference: A situation in which you can measure changes in position from your point of view. Frame of Reference: A situation in which you can measure changes in position from your point of view. Must be constant during calculations Must be constant during calculations

3. Displacement cont… If an object moves from one position to another, the length of the STRAIGHT line drawn from its initial position to the object’s final position is called the Displacement. If an object moves from one position to another, the length of the STRAIGHT line drawn from its initial position to the object’s final position is called the Displacement. Displacement = x f – x i Displacement = x f – x i Displacement does not always equal distance traveled. Displacement does not always equal distance traveled. Why? Why? Displacement can be positive or negative. Displacement can be positive or negative. Why? Why?

4. Displacement

5. Cards If you drive 10 miles north, 5 miles east, 12 miles south, and 5 miles west, what is your displacement? If you drive 10 miles north, 5 miles east, 12 miles south, and 5 miles west, what is your displacement? 32 miles north 32 miles north 22 miles south 22 miles south 2 miles south 2 miles south

6. Velocity Knowing the speed is important when evaluation motion. Knowing the speed is important when evaluation motion. Average speed is defined as the displacement divided by the time interval during when the displacement occurred. Average speed is defined as the displacement divided by the time interval during when the displacement occurred. Units are meters per second or m/s Units are meters per second or m/s Can be positive or negative (time is always positive) Can be positive or negative (time is always positive) MUST BE DESCRIBED WITH A DIRECTION MUST BE DESCRIBED WITH A DIRECTION V avg = x/ t= (x f - x i ) / (t f - t i ) V avg = x/ t= (x f - x i ) / (t f - t i ) f stands for final and i for intial

7. Sample Problem P 44 P 44 During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What distance does Andra cover in 137 s? During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What distance does Andra cover in 137 s? Given? Given? Unknown? Unknown?

8. Cards If you travel 140 meters at 7.0 m/s on your huffy 18 speed, how long would it take to the 140 meters? If you travel 140 meters at 7.0 m/s on your huffy 18 speed, how long would it take to the 140 meters? 980 seconds 980 seconds 20 seconds 20 seconds.05 seconds.05 seconds

9. Speed vs. Velocity Velocity has a magnitude and direction. Speed lacks direction. Velocity has a magnitude and direction. Speed lacks direction. During physics class, we use velocity. During physics class, we use velocity. Meaning… if a direction is given, report the direction or sign. Meaning… if a direction is given, report the direction or sign.

10. Velocity on graphs On a graph, there is an x axis and y axis. On a graph, there is an x axis and y axis. How do you find slope in terms of x and y? How do you find slope in terms of x and y? What if the y axis is the position in meters of and object and x axis is the time of the moving object, what would the slope be? What if the y axis is the position in meters of and object and x axis is the time of the moving object, what would the slope be? What do we call this slope? What do we call this slope?

11. Velocity on Graphs Instantaneous velocity may not be the same as average velocity.

12. Acceleration The quantity that describes the rate of change of velocity in a given interval is called acceleration. The quantity that describes the rate of change of velocity in a given interval is called acceleration. A avg = v / t = (v f – v i ) / (t f – t i ) A avg = v / t = (v f – v i ) / (t f – t i ) Can be positive or negative depending on how velocity changes. Can be positive or negative depending on how velocity changes. Units are (m/s) / s = m/s 2 Units are (m/s) / s = m/s 2 Has direction and magnitude Has direction and magnitude

13. Acceleration as a slope On a graph of velocity versus time, the slope equals the graph as seen in our previous section for velocity on a position- time graph. On a graph of velocity versus time, the slope equals the graph as seen in our previous section for velocity on a position- time graph.

14. Velocity and Acceleration Depending on if V i or a is positive or negative, the object can be speeding up or slowing. If a is every zero, then the object could be at rest or having a constant velocity. Depending on if V i or a is positive or negative, the object can be speeding up or slowing. If a is every zero, then the object could be at rest or having a constant velocity. Check page 51 for a table to help you understand this concept. Check page 51 for a table to help you understand this concept. Same sign on A and V i = speeding up. Same sign on A and V i = speeding up. Would a negative velocity with negative acceleration be speeding up or slowing down? Would a negative velocity with negative acceleration be speeding up or slowing down?

15. Cards Describe the motion of an object starting at rest and has a negative acceleration. Describe the motion of an object starting at rest and has a negative acceleration. Object is speeding up Object is speeding up Object is slowing down Object is slowing down Object is not moving Object is not moving

16. Motion with Constant A When acceleration is constant, velocity increases by the same amount during each time interval. When acceleration is constant, velocity increases by the same amount during each time interval. Because velocity increases by the same amount each time interval, displacement increases by the same each time interval. Because velocity increases by the same amount each time interval, displacement increases by the same each time interval.

17. Displacement with constant uniform Acceleration X= ½ ( v i + v f ) t X= ½ ( v i + v f ) t Displacement = ½ (initial velocity + final velocity) * (time interval) Displacement = ½ (initial velocity + final velocity) * (time interval) Do units work out? Why the ½? Do units work out? Why the ½? A racing car reaches a speed of 42 m/s. It then begins a uniforms negative acceleration, using its parachute and braking system, and comes to a rest 5.5 s later. Find how far the car moves while stopping. P 53. A racing car reaches a speed of 42 m/s. It then begins a uniforms negative acceleration, using its parachute and braking system, and comes to a rest 5.5 s later. Find how far the car moves while stopping. P 53. Given? Unknown? Given? Unknown?

18. V f with uniform A V f = v i + a * t V f = v i + a * t Final velocity = initial velocity + acceleration x time interval Final velocity = initial velocity + acceleration x time interval Units? Units? P 54 P 54

19. Cards Using the last equation, if V i and a are negative while t is positive, what sign would V f have? Using the last equation, if V i and a are negative while t is positive, what sign would V f have? No sign No sign Negative Negative positive positive

20. X with uniform A Displacement can be found out knowing the final velocity. Displacement can be found out knowing the final velocity. X =v i *t + ½ a (t) 2 X =v i *t + ½ a (t) 2 Displacement = initial velocity x time + ½ acceleration x (time interval) 2 Displacement = initial velocity x time + ½ acceleration x (time interval) 2 Units? Units?

21. Velocity and displacement A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s 2 for 15 s before takeoff. What is its speed at take off? How long must the runway be for the plane to be able to take off? A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s 2 for 15 s before takeoff. What is its speed at take off? How long must the runway be for the plane to be able to take off? Givens? Givens? Unknowns? Unknowns? P 55 P 55

22. Where do these come from? There are lots of kinematic equations to describe motion. There are lots of kinematic equations to describe motion. We have skipped the derivation of these equations for ease. They can be found in chapter 2. This is where you will understand where they come from. We have skipped the derivation of these equations for ease. They can be found in chapter 2. This is where you will understand where they come from.

23. VfVfVfVf Final velocity after any displacement Final velocity after any displacement V f 2 = V i 2 + 2 a x V f 2 = V i 2 + 2 a x Final velocity 2 = initial velocity 2 + 2 x acceleration x displacement Final velocity 2 = initial velocity 2 + 2 x acceleration x displacement Units? Units? A person pushing a stroller starts from rest, uniformly accelerating at a rate of.500 m/s 2. What is the velocity of the stroller after it has traveled 4.75 m? A person pushing a stroller starts from rest, uniformly accelerating at a rate of.500 m/s 2. What is the velocity of the stroller after it has traveled 4.75 m? Given? Unknown? Given? Unknown?

24. Free fall When objects are in a vacuum (lack of air), they will fall as the exactly same rate. When objects are in a vacuum (lack of air), they will fall as the exactly same rate. When objects are close to the surface of a planet, they fall at a constant rate in the absence of air resistance. When objects are close to the surface of a planet, they fall at a constant rate in the absence of air resistance. Such motion is called free fall. Such motion is called free fall.

26. Free fall Rate of free fall on earth is due to gravity Rate of free fall on earth is due to gravity Gravity or g is 9.81 m/s 2 Gravity or g is 9.81 m/s 2 Because we use direction in class, we have to note the direction of g. Gravity is towards the center of the earth. This is a downward or negative direction. Because we use direction in class, we have to note the direction of g. Gravity is towards the center of the earth. This is a downward or negative direction. A = -g = -9.81/s 2 A = -g = -9.81/s 2

27. What goes up must … Come down. We know from everyday experiences that what is thrown up, will come down. This is due to gravity (- 9.81). Objects thrown will always experience g. Come down. We know from everyday experiences that what is thrown up, will come down. This is due to gravity (- 9.81). Objects thrown will always experience g. It is hard to think of an object moving upward as having a negative acceleration, this means the object is just slowing down (opposite signs). It is hard to think of an object moving upward as having a negative acceleration, this means the object is just slowing down (opposite signs). After an object reaches the top of a path, the object falls back to earth and acceleration and velocity are in the same direction, there for the object speeds up. After an object reaches the top of a path, the object falls back to earth and acceleration and velocity are in the same direction, there for the object speeds up.

28. Free fall

29. Falling object Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upwards. If the volleyball starts at 2.0 meters above the floor, how long will it be in the air before it strikes the floor? Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upwards. If the volleyball starts at 2.0 meters above the floor, how long will it be in the air before it strikes the floor? Given? Given? Unknown? Unknown? Equation? Equation? P 63 P 63