Describing and Measuring Motion

1. Describing and Measuring Motion

2. Changing Motion Challenge

3. Motion • How do you know if you are moving? • If you’ve ever traveled on a train, you know you cannot always tell if you are in motion. Looking at a building outside the window helps you decide. Although the building seems to move past the train, it’s you and the train that are moving. • However, sometimes you may see another train that appears to be moving. Is the other train really moving, or is your train moving? How do you tell?

4. Motion • a change in position, or location of a place or object, over a certain amount of time • relies on a frame of reference or something assumed to be stationary • is relative to a frame of reference • i.e. – you may be stationary as you sit in your seat, but you are moving 30 km/sec (≈19 mi/sec) relative to the Sun • Relative Motion Simulation

5. Relative Motion • Are you moving as you read this page? • The answer to that question depends on your reference point. When your chair is your reference point, you are not moving. But if you choose another reference point, you may be moving. • Suppose you choose the sun as a reference point instead of your chair. If you compare yourself to the sun, you are moving quite rapidly. This is because you and your chair are on Earth, which moves around the sun. • Earth moves about 30 kilometers every second. So you, your chair, a book, and everything else on Earth move that quickly as well. Going that fast, you could travel from New York to Los Angeles in about 2 minutes! Relative to the sun, both you and your chair are in motion. But because you are moving with Earth, you do not seem to be moving.

6. 6 meters Speed • the rate at which an object moves • a measure of how fast something moves, or the distance it moves, in a given amount of time • Formula: • typically expressed in units of m/s • is considered average when taking into account the total distance covered and the total time of travel • is considered constant when it does not change • is considered instantaneous when it represents a specific instant in time S = d t 00:00. 0 1 2 3 4 5 6 What is the ball’s speed?

7. Interesting Speeds

8. Practice Problems - Speed • If you walk for 1.5 hours and travel 7.5 km, what is your average speed? 2. Calculate the speed of a bee that flies 22 meters in 2 seconds. S = d t 7.5 km 5 km hr S = = 1.5 hr 11 m sec 22 m S = d t S = = 2 sec

9. 120 100 80 Distance (meters) 60 40 20 0 90 100 30 40 50 60 70 80 10 20 Time (seconds) Distance-Time Graph Shows how speed relates to distance and time C This distance-time graph will show a student’s speed as he returns to class after lunch. What is the speed from B-C ? What is the speed from A-B ? A B What is the student’s average speed? What is the speed from 0-A ?

10. Describe What’s Happening(distance-time graphs) Constant speed; away from starting point Constant speed; no movement Constant speed; toward the starting point

11. Velocity • the rate of change of an object’s position • speed in a given direction • is considered constant when speed and direction do not change • changes as speed or direction changes • is a vector • can be combined • Example • If you are walking at a rate of 1.5 m/s up the aisle of an airplane that is traveling north at a rate of 246 m/s, your velocity would actually be 247.5 m/s north What is the formula for calculating velocity? 10 m/s Does the ball have a constant velocity? 29 m/s east 10 m/s 29m/s west

12. Velocity versus Speed • Speed refers to how quickly an object moves • Velocity is defined as speed in a given direction or rate of change of position (displacement over time). v = x/t • Velocityrefers to both the speed and direction of motion of an object. • Negative velocity means the object is moving in the opposite direction • Motion atconstant 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

13. Acceleration • the rate at which velocity changes • is a vector • occurs when something is speeding up (+), slowing down (-), or changing direction • Formula: • typically expressed in units of m/s2 • is always changing when traveling in a circle - centripetal a = vf – vi t 10 m/s Is the ball accelerating? Describe the car’s acceleration Describe the car’s acceleration 10 m/s a = 50 m/s – 0 m/s = 10 m/s2 5 s a = 0 m/s – 10 m/s = -5 m/s2 2 s

14. Understanding Acceleration When dropped, the ball will accelerate toward the center of the Earth at a rate of 9.8 m/s2 because of gravity. What will be the ball’s acceleration at each second? 9.8 19.6 29.4 39.2 49.0

15. Practice Problems - Acceleration • Tina starts riding her bike down a hill with a velocity of 2 m/s. After six seconds, her velocity is 14 m/s. What is Tina’s acceleration? 2. A motorcyclist goes from 35 m/s to 20 m/s in five seconds. What was his acceleration? a = vf – vi t 14 m/s - 2m/s 2 m s2 a = = 6 s a = vf – vi t 20 m/s - 35 m/s -3 m s2 a = = 5 s

16. Velocity –Time Graph • Velocity Time Graph is used to show acceleration • Time is on the x-axis • Velocity is on the y-axis

17. Time Velocity Graph • Rising line shows where the acceleration is positive, the steeper the line, the greater the acceleration • The flat line shows an interval of no acceleration, velocity is not changing – constant velocity • The falling line shows where the acceleration is negative, velocity is decreasing

18. Positive acceleration Negative acceleration

19. 12 10 8 Velocity (meters/second) 6 4 2 0 90 100 30 40 50 60 70 80 10 20 Time (seconds) Velocity-Time Graph Shows how acceleration relates to velocity and time This velocity-time graph will show a student’s acceleration as she returns to class after lunch. Describe the student’s acceleration as she travels to class?