TOPIC I .

1. Mechanics TOPIC I.

2. Kinematics • I. • • Branch of Mechanics that deals with motion without regard to forces producing it. • A. Distance and Displacement • 1. Distance: the total length of the path that an object travels. • a. A scalar quantity • b. SI Unit is the meter (m) • c. length, width, and height are all distances!

3. 2. Displacement: the change in position of an object. • a. A vector quantity because it has a both magnitude and direction • b. “As the crow flies” (magnitude is a straight line from initial to final positions) C Look!!! A Right Triangle!!! Displacement  A B

4. c. SI unit for displacement is the meter (same as for distance) • d. magnitudes for displacement and distance are NOT usually the same! Example: Displacement 10 m End • What is the distance traveled? 7 m 44 m 10 m 7 m 10 m Start

5. • What is the displacement? 10 m End A Right Triangle has been formed! 7 m 10 m Use the Pythagorean Theorem! 7 m 10 m Start (10 m)2 + (14 m)2 = c2 100 m2 + 196 m2 = c2 296 m2 = c2 17.2 m = c

6. B. Speed and Velocity • 1. Speed: the distance an object moves per unit time • a. Speed is a scalar quantity • b. SI units are meters per second (m/s) • c. other units for speed: • kilometers per hour (km/hr or kph) • d. Formula for average speed (v): • d = distance (m) • t = time (s) _

7. Example: Speed Conversion! • If you were traveling 170 km/hr, what is your speed in meters per second (m/s)? Answer: 47.2 m/s What is this speed in MPH? Would you get a ticket? Answer: 105.6 mph YES!!

8. 2. Velocity: the time rate of change of an object’s displacement • a. A vector quantity since it adds direction to speed • b. Units: (m/s) but with a direction attached • c. It is possible that two objects can have the same speed, but different velocities + = velocity

9. d. Finding Velocity Mathematically (using formulas) • 1. Basic formula: average velocity displacement time Reference Tables!! 2. Also: initial velocity final velocity

10. Examples: Velocity • What is the average velocity of a car that travels 2450 meters to the east in 1 minute? • How long does it take a jet to fly 1 kilometer if its velocity is 250 m/s North?

11. C. Acceleration • 1. Definition: is the rate of change of velocity. • • “how fast something is speeding up or slowing down” • • Example: gas pedal = increasing speed • (accelerator)

12. 2. Acceleration is a vector quantity! Always has a direction attached! • 3. Formula:

13. 4. Units for acceleration using dimensional analysis:

14. 5. Finding Acceleration Mathematically • a. Basic formula for “change in velocity per unit time”: • • since Δv= vf – vi substitute into the above equation:

15. • solve for final and initial velocities: a Speed (m/s) t Time (sec)

16. Example: Acceleration • The space shuttle starts from rest and speeds up to 10000 kilometers per hour in 90 seconds. What is the acceleration of the shuttle? • A truck speeds up at a rate of 10 m/s2. If the truck was initially travelling 15 m/s, how fast would it be travelling after 20 seconds?

17. Example: Solve for a • Now d can be expressed as: • b. Acceleration with displacement or distance (d):

18. Example: Find Displacement • A car decelerates rapidly from 26.94 m/s and comes to rest in 3.25 s. The deceleration provided by the brakes is 8.3 m/s2. How far does the car travel while stopping? Assume the car was traveling South.

19. Warm Up #6//14 • A school bus slowly drives through Carrollton at 35 mi/hr. • What is the bus speed in meters per second? • What how far will the bus travel in 10 seconds? • What is the acceleration of the bus if it comes to a stop in 5 seconds?

20. Example: Find a • In a drag race, two beat up, old, Honda Civics with need to cover 500 meters. The cars start from rest and reach top speed in 8 seconds. What is the acceleration of the cars?

21. c. If time is NOT known: d. Bottom Line:  any piece of unknown information can be found if 3 variables in any situation are known:d, vi , vf, t , and a

22. Example: Find Final Velocity • A car accelerates from 10 m/s at a rate of 5 m/s2 over the course of 100 meters. What is the car’s final velocity? Assume the car was traveling West.

23. Example: Find Distance • A sled moving at 5 m/s decelerates to rest at a rate of 2 m/s2. How far did the sled travel while it was coming to a stop?

24. e. Many times, objects start from rest, causing initial velocity (vi) to be zero! • • This makes equations easier!    

25. D. Graphing Motion • 1. Distance vs. Time • a. Constant Speed Positive Direction Distance Negative Direction Time

26.  Increasing Speed • b. Changing Speed (acceleration) Distance Distance Time Decreasing Speed  Time

27. c. No Movement Distance Time

28. 2. Speed Versus Time Graphs Speed (m/s) Speeding UP!! Time (sec) a. Constantor UniformAcceleration (speed is increasing at a steady rate)

29. Speed vs. Time Slowing DOWN!! Speed (m/s) NEGATIVE Acceleration Time (sec) b. Constant or UniformDeceleration (speed is decreasing at a steady rate)

30. Speed vs. Time Steady Speed! Speed (m/s) Time (sec) c. NO Acceleration: Velocity is constant!

31. 3. Slopes of Motion Graphs or

32. Practice:

33. • Calculate the slope of the graph… (units!) • • What was the velocity at 2.5 seconds? • • What time was the object moving at 25m/s? • • What does the slope of the graph mean?

34. 4. Positive and Negative Motion Graphs

35. D. Freely Falling Objects • 1. In a space all objects will fall or accelerate toward the most dominant source of gravity (usually a large mass). • 2. Earth causes falling objects accelerate at a constant 9.81m/s2 toward the planet’s center. •  symbol g

36. 3. The equations for motion are usable in the cases of freely falling objects: replace a with g. • note what happens to these equations when an object is dropped “from rest” 4. ALL Free falling objects are instantaneously accelerated or decelerated at a rate of g the moment they are released Cat