TOPIC I.

I. Branch of Mechanics that deals with motion without regard to forces producing it. 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!

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) AB C Displacement  Look!!! A Right Triangle!!!

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

What is the displacement? 10 m 7 m 10 m Start End A Right Triangle has been formed! Use the Pythagorean Theorem! (10 m) 2 + (14 m) 2 = c m m 2 = c m 2 = c m = c 10 m

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) _

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: mph YES!!

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

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

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?

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

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

4. Units for acceleration using dimensional analysis:

5. Finding Acceleration Mathematically a. Basic formula for “change in velocity per unit time”: since Δv = v f – v i substitute into the above equation: since Δv = v f – v i substitute into the above equation:

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

Example: Acceleration The space shuttle starts from rest and speeds up to kilometers per hour in 90 seconds. What is the acceleration of the shuttle? A truck speeds up at a rate of 10 m/s 2. If the truck was initially travelling 15 m/s, how fast would it be travelling after 20 seconds?

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

Example: Find Displacement A car decelerates rapidly from m/s and comes to rest in 3.25 s. The deceleration provided by the brakes is 8.3 m/s 2. How far does the car travel while stopping? Assume the car was traveling South.

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?

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?

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

Example: Find Final Velocity A car accelerates from 10 m/s at a rate of 5 m/s 2 over the course of 100 meters. What is the car’s final velocity? Assume the car was traveling West.

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

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

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

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

c. No Movement Distance Time

2. Speed Versus Time Graphs Speed (m/s) Time (sec) a. Constant or Uniform Acceleration (speed is increasing at a steady rate) Speeding UP!!

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

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

3. Slopes of Motion Graphs or

Practice:

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

4. Positive and Negative Motion Graphs

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/s 2 toward the planet’s center.  symbol g

4. ALL Free falling objects are instantaneously accelerated or decelerated at a rate of g the moment they are released 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” note what happens to these equations when an object is dropped “from rest” Cat