Intro to kinematics September 12, 2016 Do Now: Reflect on the 1st unit. What are your goals for the second unit? How will you achieve them. Write a few sentences on a paper to be turned in at end of class. September 12, 2016

Goal To describe motion using vocabulary, equations, and graphs.

How would you describe an a Object’s motion? The answer depends on your perspective -- your frame of reference Example: Even while sitting in the classroom appearing motionless, you are moving very fast. • Rotating 0.4 km/s (0.25 mi/s) around the center of the Earth • Revolving 30 km/s relative to the Sun Revolving 250 km/s with the solar system around the center of the milky way galaxy Moving 600 km/s with the Milky Way away from the center of the universe, towards the constellation Hydra The Sea Serpent

When we discuss the motion of something, we describe its motion relative to something else. A frame of reference is a perspective from which a system is observed together with a coordinate system used to describe motion of that system. Example: You drive your car home from school at speed of 30 mph. … your frame of reference is relative to road …. Your coordinate system has a starting point (origin) at school and a positive direction towards home

We also discuss motion using simplified models, such as the particle model. The movement of an object through space can be quite complex. There can be internal motions, rotations, vibrations, etc… Example: This motion is complex! But, if we ignore the shape of the hammer and treat it as a particle moving through space, we can greatly simplify the motion – making it much easier to make predictions

How to speak ‘kinematics’ Throughout this unit, we will describe motion using three important terms: displacement, velocity, and acceleration What do you think these terms mean? Discuss with a partner, and come up with real life examples

displacement, velocity, and acceleration How to speak ‘kinematics’ Throughout this unit, we will describe motion using three important terms: displacement, velocity, and acceleration Displacement is the change in position of an object Equation: ∆x = x2 – x Units: m Velocity is the change in position per unit time Equation: v = ∆𝑥 ∆𝑡 Units: ms-1 Acceleration is the change in velocity per unit time Equation: a = ∆𝑣 ∆𝑡 Units: ms-2 How accurate were your guesses and examples? Can you think of more examples now? Which of these quantities can you ‘feel’? Justify your answer with every day examples. What do you feel?

Displacement + _ + _ P Q Distance = total length travelled Displacement = length and direction of the straight line from initial position to final position Displacement is a vector that tells us how far and in what direction an object is from its initial position. Displacement: ∆x = x2 – x1 x2 is the final position; x1 is the initial position Predict 15 minutes to here What kind of a quantity is distance? What kind of a quantity is displacement? Implicit means implied but not directly state + Often times in physics we use an implicit coordinate system. _ + _

Displacement Problems 1. A ball starts at position -4 m and goes to position 1m. What is its displacement? 5m (direction is positive direction, as defined by number line) 2. What does negative displacement mean? Will you ever have a negative distance? Why or why not? Turn & talk, then answer: 2 min Get them to explain why / how they know. A ball starts at position 3 m, goes to position -3m, then rolls to position -1m. What is its displacement? What is the total distance traveled? -4 m 8m

Displacement Problems A race car travels around a circular track of radius 100 m. The car starts at position O and travels to position P. When the car gets to position P, What distance has it traveled? What is its displacement? Turn and talk, then cold call 2 min Hint 2: You may use your phones to look up any formulas about circles, if necessary. Hint 1: Use the 360o coordinate system

Displacement Problems A race car travels around a circular track of radius 100. m. The car starts at position O and travels to position P. distance When the car gets to position P, What distance has it traveled? Distance = (1/4)(2πr) = 157 m What is its displacement? displacement Turn and talk, then cold call 2 min Displacement = √ (1002 + 1002) = 141 m Tan-1(100/100) = 45o Apply coordinate system: 45o+270o = 315o Final answer: 141 m, 315o

Velocity 𝒗avg = ∆𝒙 ∆t = 𝒙𝟐 −𝒙𝟏 𝒕𝟐−𝒕1 Velocity is a measure of how fast an object moves through a displacement 𝒗avg = ∆𝒙 ∆t = 𝒙𝟐 −𝒙𝟏 𝒕𝟐−𝒕1 Velocity is a vector, and it has the same direction as the displacement. Units: m/s Back to the earlier problem If the ball rolls from position 3m, to position -3 m, then to -1 m in a time interval of 2 seconds, what is its average velocity? 25 min + 10 min ‘start time’ V = −1𝑚 −3𝑚 2𝑠 = -2 m/s

Velocity Terminology Speed vs. Velocity Speed is distance/time, and it is a scalar. Velocity is displacement/time, and it is a vector. Often, speed and velocity have the same magnitude, but sometimes they differ. Can you think of an example? Back to the same problem! Speed = distance/time = 8m/2sec = 4 m/sec Velocity = displacement/time = -4 m/ 2sec = -2 m/s

Velocity Terminology Speed vs. Velocity Speed is distance/time, and it is a scalar. Velocity is displacement/time, and it is a vector. Average vs. Instantaneous Average speed and average velocity are calculated over a period of time, using the formulas above Instantaneous speed and instantaneous velocity refer to the speed or velocity at a specific instant of time (Δt 0) No algebraic formula for instantaneous speed or velocity, but we can estimate it graphically. Calculus invented for these problems. Will do graphically solving next class. Connection: Your car’s speedometer tells you instantaneous speed. What else would you need to know to find instantaneous velocity? A compass for direction!

Speed & Velocity Problems A race car drives along a circular track of radius 100.m from position O and back again in 12 sec. A boat travels 142 m W then 120 m S. The trip lasts 24 seconds. Calculate the boat’s average speed and average velocity. What is the race car’s average speed? What is the race car’s average velocity? Speed = distance /time = 2πr / t = 52 m/s Velocity = displacement/time = 0 m/s! Speed = (142m + 120 m)/24 = 11 m/s Velocity = √(1422 + 1202) /24 = 7.7 m/s tan-1(120/142)= 40o add 180o = 220o

Acceleration Acceleration is a measure of how quickly an object change’s its velocity. Units = 𝑚 𝑠 𝑠 = m/s2 a = Δ𝑣 Δ𝑡 = 𝑣2−𝑣1 𝑡2−𝑡1 We have acceleration whenever velocity changes … speeding up slowing down changing direction We won’t use the word ‘deceleration’ in this class! 40 min + 10 min ‘start time’ An acceleration of 3m/s2 means that an object’s velocity changes by 3m/s every second. If v = -6 m/s at time = 0 s, then what would it equal at time t = 1s, t = 2s, t = 3s, etc? at t= 1s, v = -3 m/s at t = 2s, v = 0 m/s at t = 3 s, v = 3 m/s

Acceleration Practice time! + + + - - - - + Like displacement and velocity, acceleration is a vector! Acceleration is positive when the change in velocity makes the object move faster in the positive direction or slower in the negative direction. Practice time! NOTE! You can substitute the word positive for another directional term, such as ‘up’ or ‘East’. You would then substitute the opposite direction (‘down’ or ‘West’) for the negative term. Work in table groups in hallway. Door is origin (position = 0). Left as we exit our room is negative direction, right as we exit is positive direction. Give your partner a starting position (+/-), a starting velocity (+/-) and an acceleration (+/-) and have them act it out. Each person does two scenarios then switch. Motion Velocity Acceleration Speeding up in positive direction Slowing down in a positive direction Speeding up in a negative direction Slowing down in a negative direction + + + - - - Do first example, have class turn and talk for others. Ask the kids, how do they know what way velocity is? - + Memory aid: Speeding up occurs whenever velocity and acceleration ‘work together’ (have same signs). Slowing down occurs whenever velocity and acceleration are working against each other (have opposite signs)

Acceleration Problems Use your kinematic vocabulary to describe the following motions. Be sure to use the words velocity and acceleration. For added challenge, try describing speed, position, and displacement! A train traveling north slows to a stop. A car starts driving from rest and speeds up in a positive direction. A ball is thrown up into the air. It rises then falls back to the same starting position. The train was moving with velocity to the North, but accelerating South, which meant that the train was slowing down. Eventually, the instantaneous velocity reached zero. The displacement was North. The car started with an instantaneous velocity of zero. It accelerating in the positive direction, making it speed up with a positive velocity. The displacement was positive. Give them an example. The ball started at position zero. As it rose in the air, it had a upwards velocity and a downward acceleration, making it slow down. The instantaneous velocity was zero at the top of the motion. As it fell, it had a downwards velocity and a downwards acceleration, making it speed up as it fell. Its overall displacement was zero because it came back to where it started.

Closure What were your biggest take-aways from our learning objectives? How does what we did today relate to our overall unit objective? How does what we did today relate to our learner profile trait? How does what we did today relate to our TOK connection? 65 min + 10 min ‘start time’

Exit Ticket Write on your ‘do now’ paper. 1) Make up a problem and solve a problem that demonstrates your understanding of the differences between: Distance and displacement - or - Speed and velocity 2) Make up and solve a problem that demonstrates your understanding of the directions of velocity and acceleration 65 min + 10 min ‘start time’