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UNIT 1 Motion Graphs LyzinskiPhysics x t Days 1 - 2

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The purpose of this chapter is to learn the 1 st step of Mechanics (the study of motion) which is KINEMATICS (the study of motion with no regards to what is causing the motion). The study of what is “causing” the motion is known as dynamics, and we will study this in a later chapter.

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- Mechanics KINEMATICS DYNAMICS - Electricity - Magnetism - Optics - Waves PHYSICS A “description” of motion A study of what “causes” motion

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Day #1 * Distance * Speed * Scalars * d-t graphs

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Definition Distance (d) – the length of the path followed by an object * If an object’s path is straight, the distance is the length of the straight line between start and finish. ** If an object’s path is NOT straight, the distance is the length of the path if you were to “straighten it out” and measure it the way you would measure the length of a curved shoelace. start finish start finish

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Using the number line above, what would be the distance travelled if an object travelled from ….. - A to B - A to C - A to C and then back to A - C to B, passing through A BC A meters 1m 4m 4m + 4m = 8m 4m + 1m = 5m

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5 yd 12 yd A B C Sally and Timmy are at point A. Sally walks directly to point C (taking the shortest path). Timmy also takes a “shortest path”, but has to stop at point B for lunch first. How much further has Timmy walked when he arrives? 4 yd

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Definition Average Speed (s) – the distance travelled during a time interval divided by the elapsed time. s = d/ t ( or s=d/t) Since t = t 2 – t 1, if t 1 = 0, then t = t 2 – 0 = t 2 = t

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Larry walks from point B to point C, and then goes directly to point A. If he walks at an average speed of 6 mph, how long does the trip take him? BC A miles d = 3mi + 4mi = 7mi s = 6 mi/h s = d/t t = d/s = (7mi)/(6mi/h)=1.17h 1 h, 10 min Use appropriate units

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Larry runs from point A to point B in 5 minutes and then proceeds to jog directly to point C, taking his time in 30 additional minutes. Find… BC A km a)Larry’s average speed during the first portion of the trip. b)The average speed during the second portion of the trip. c)Larry’s average speed for the entire trip. s = d/t = (1km)/(5min) = 0.2 km/min = 12 km/h s = d/t = (3km)/(30min) = 0.1 km/min = 6 km/h s = d/t = (4km)/(35min) = km/min = 6.86 km/h

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Definition Scalar – a quantity that has a magnitude only, no direction. * YES, scalars can have units. ** What scalars have we learned about thus far? ___________ ____________ ___________ distance speedtime I thought time could march backward?

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d-t graphs Constant speed Speeding UP Constant Speed (faster!) Slowing Down At rest t (sec) d (m) B C E A D F

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Speed on a d-t graph can be found by taking the _______________. SLOPE s AB = rise/run = (30-0m) / (10-0s) = 3 m/s s CD = rise/run = (100-50m) / (20-15s) = 10 m/s t (sec) d (m) B C E A D F

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Open to in your Unit 1 packet 520 – 170yd = 350 yd (approximately) 1 d-t graphs CANNOT have sharp points NOTHING CAN STOP INSTANTANEOUSLY!!

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Day #2 * Position * Displacement * Average Velocity * Vectors * x-t graphs

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Definition Position (x) – the location of an object with respect to a specified reference point. *We choose this reference point to be the origin of a coordinate system A km The position of particle “A” is either x = -3 or x = 6, depending on which reference point (or origin) you use.

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Definition Displacement ( x) – the change in an object’s position during a time interval. x = x 2 – x 1 or x = x f – x i *Displacement must have both a magnitude (size) and a direction (right, left, up, down, north, south, etc). These are all VECTORS. What’s a vector?

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Using the number line above, find the distance travelled and the displacement in moving from - A to B - C to A - A to C and then back to A - C to B, passing through A BC A meters 1m, 1m [right] 4m, 4m [left] 8m, 0m 4m, 3m [left] x = 1 – (1m) = 0m x = (-2) – (1m) = -3m OR 3m [left]

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Definition Average Velocity ( v ) – the displacement of an object divided by the elapsed time. v = x/ t ( or v= x/t)

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AD B C Sam runs the 400m dash. He starts and finishes at point A, travelling one complete circuit around the track. Each section of the track is 100m long. His average speed during each interval are as follows. AB: 7 m/s BC: 8 m/s CD: 6 m/s DA: 7.5 m/s s = d/t t = d/s = 100m/7sec = sec 100m/8sec = 12.5 sec 100m/6sec = sec 100m/7.5sec = sec s = d/t = (400m)/(56.786s) = 7.04 m/sec Find Sam’s avg. speed and avg. velocity for the entire trip. Avg Velocity = 0 since x = 0 for the entire trip.

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AD B C Sam runs the 400m dash. He starts and finishes at point A, travelling one complete circuit around the track. Each section of the track is 100m long. His average speeds during each interval are as follows. AB: 7 m/s, sec BC: 8 m/s, 12.5 sec CD: 6 m/s, sec DA: 7.5 m/s, sec m Find Sam’s average speed and average velocity for the 1 st half of the race. s = d/t t = d/s = 200m/( s) = 7.47 m/s v = x/t = (104.94m )/( s) = 3.92 m/sec

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Definition Vector – a quantity that has both magnitude AND a direction … oh yeh! * YES, vectors can have units. ** What vectors have we learned about thus far? ____________ ________________ ___________ position displacement velocity

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Scalars vs. Vectors has magnitude & direction (example: 15 cm east) has a magnitude only (example: 6 ft) 1 2 A B Displacement is NEVER greater than distance traveled! Displacement: Distance:

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Scalars vs. Vectors (continued) has magnitude & direction (example: 15 mi/h North) has a magnitude only (example: 30 km/h) If an object STARTS & STOPS at the same point, the velocity is ZERO! (since the displacement is zero) Velocity: Speed: km 7 km Total time for the trip from 1 to 2: 1 hr Speed = 31 km/h Velocity = 25 km/h at 16 o NE 25 km 16 o Don’t worry about this notation for this test

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x-t graphs t (sec) x (m) t 1 t 2 t 3 x2x1x3x2x1x3 B C D A Constant speed (Constant + velocity, or constant velocity in the + direction) Slow down, speed up, slow down, speed up 2 moments where the object is “at rest” (for a moment)

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How to get the position (x) at a certain time (t) off an x-t graph x(m) t (s) Example: What is the position at t = 30 seconds? Go over to t = 30. Find the pt on the curve. Find the x value for this time. 24m

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How to calculate the displacement between two times on an x-t graph x(m) t (s) Example: What is the displacement from t = 10 to t = 40? Find x 1 Find x 2 Use x = x 2 - x 1 = + 7 m 10 m 17 m

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How to find the distance traveled between two times on an x-t graph. x(m) t (s) Example: What is the distance traveled from t = 10 to t = 40? Find the distance traveled in the + direction. Find the distance traveled in the - direction. Add them together. (27 m) 17 m 10 m

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Understand the difference between velocity and speed on an x-t graph. x(m) t (s) Example: What is the average speed from t = 10 to t = 40 seconds? dist = 27 m (previous slide) Avg. Speed = dist/ t = 27m / 30 sec = 0.9 m/s 17 m 10 m

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Understand the difference between velocity and speed on an x-t graph. x(m) t (s) Example: What is the average velocity from t = 10 to t = 40 seconds? Avg. Velocity = slope = x/ t = + 7 / 30 sec = m/s x = + 7 m (previous slide)

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Will avg. velocity EVER be greater than avg. speed? NO!!! Will avg. velocity EVER be equal to avg. speed? YES!!! When the path travelled was one-way, in a straight line.

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Negative Average Velocity? x(m) t (s) Avg. vel. = slope = rise/run = -7 m / 20 = -.35 m/s Example: What is the average velocity from t = 20 to t = 40 seconds? Since the objects displacement is in the NEGATIVE direction, so is its average velocity.

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-10 m avg velocity = slope = -15m / 6sec = -2.5 m/s s = |v| = 2.5 m/s At rest at t = 0 and t = 12 sec Open to in your Unit 1 packet 1 2) 3) 4)

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x = x 2 – x 1 = (-10m) – (10m) = -20m (approximately) 5) 6) Speeding up, const negative vel, slowing down, speeding up, const positive velocity(slow), speeding up, constant positive velocity (fast)

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