2The purpose of this chapter is to learn the 1st 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.
3PHYSICS - Mechanics - Electricity - Magnetism - Optics - Waves KINEMATICS- MechanicsA “description” of motion- ElectricityDYNAMICS- MagnetismA study of what “causes”motion- Optics- Waves
5Definition Distance (d) – the length of the path followed by an object * If an object’s path is straight, the distance is the length ofthe straight line between start and finish.** If an object’s path is NOT straight, the distance is thelength of the path if you were to “straighten it out” andmeasure it the way you would measure the length of acurved shoelace.startfinishstartfinish
6BCAmetersUsing the number line above, what would be the distance travelled if an object travelled from …..1m- A to B- A to C- A to C and then back to A- C to B, passing through A4m4m + 4m = 8m4m + 1m = 5m
74 yd B 12 yd 5 yd C A 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
8DefinitionAverage Speed (s) – the distance travelled during a time interval divided by the elapsed time.s = d/Dt(or s=d/t)Since Dt = t2 – t1, if t1 = 0, thenDt = t2 – 0 = t2 = t
91 h, 10 min d = 3mi + 4mi = 7mi s = 6 mi/h BCAmilesLarry 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?d = 3mi + 4mi = 7mis = 6 mi/hs = d/t t = d/s = (7mi)/(6mi/h)=1.17h1 h, 10 minUse appropriate units
10BCAkmLarry 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…Larry’s average speed during the first portion of the trip.The average speed during the second portion of the trip.Larry’s average speed for the entire trip.s = d/t = (1km)/(5min) = 0.2 km/min = 12 km/hs = d/t = (3km)/(30min) = 0.1 km/min = 6 km/hs = d/t = (4km)/(35min) = km/min = 6.86 km/h
11Definition distance speed time Scalar – a quantity that has a magnitude only, no direction.* YES, scalars can have units.** What scalars have we learned about thus far?___________ ____________ ___________distancespeedtimeI thought time could march backward?
12d-t graphs E F D C B A Constant speed Speeding UP Constant Speed (faster!)Slowing DownAt restt (sec)d (m)BCEADF1201005030
13sAB = rise/run = (30-0m) / (10-0s) = 3 m/s t (sec)d (m)BCEADF1201005030SLOPESpeed on a d-t graph can be found by taking the _______________.sAB = rise/run = (30-0m) / (10-0s) = 3 m/ssCD = rise/run = (100-50m) / (20-15s) = 10 m/s
14Open to in your Unit 1 packet 1 d-t graphs CANNOT have sharp pointsNOTHING CAN STOP INSTANTANEOUSLY!!520 – 170yd = 350 yd (approximately)
15Day #2 * Position * Displacement * Average Velocity * Vectors * x-t graphs
16DefinitionPosition (x) – the location of an object with respect to a specified reference point.*We choose this reference point to be the origin of acoordinate system.AkmThe position of particle “A” is either x = -3 or x = 6, depending on which reference point (or origin) you use.
17These are all VECTORS. What’s a vector? DefinitionDisplacement (Dx) – the change in an object’s position during a time interval.Dx = x2 – x1orDx = xf – xi*Displacement must have both a magnitude (size) and adirection (right, left, up, down, north, south, etc).These are all VECTORS. What’s a vector?
181m, 1m [right] 4m, 4m [left] 8m, 0m 4m, 3m [left] -3 -2 -1 0 1 B C A AmetersUsing the number line above, find the distance travelled and the displacement in moving from1m, 1m [right]- A to B- C to A- A to C and then back to A- C to B, passing through ADx = 1 – (1m) = 0m4m, 4m [left]8m, 0m4m, 3m [left]Dx = (-2) – (1m) = -3m OR 3m [left]
19(or v=Dx/t) Definition Average Velocity ( v ) – the displacement of an object divided by the elapsed time.v = Dx/Dt(or v=Dx/t)
20Find Sam’s avg. speed and avg. velocity for the entire trip. BCSam 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/sBC: 8 m/sCD: 6 m/sDA: 7.5 m/sFind Sam’s avg. speed and avg. velocity for the entire trip.s = d/t t = d/s = 100m/7sec = sec100m/8sec = 12.5 sec100m/6sec = sec100m/7.5sec = secs = d/t = (400m)/(56.786s) = 7.04 m/secAvg Velocity = 0 since Dx = 0 for the entire trip.
21s = d/t t = d/s = 200m/(14.286+12.5s) = 7.47 m/s ADBCSam 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, secBC: 8 m/s, 12.5 secCD: 6 m/s, secDA: 7.5 m/s, sec100104.94mFind Sam’s average speed and average velocity for the 1st half of the race.s = d/t t = d/s = 200m/( s) = 7.47 m/sv = Dx/t = (104.94m )/( s) = 3.92 m/sec
22Definition position velocity 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?____________ ________________ ___________positiondisplacementvelocity
23Scalars vs. Vectors Displacement: has magnitude & direction (example: 15 cm east)Distance:has a magnitude only (example: 6 ft)12ABDisplacement is NEVER greater than distance traveled!
24Scalars vs. Vectors (continued) Velocity:has magnitude & direction (example: 15 mi/h North)Speed:has a magnitude only (example: 30 km/h)12Total time for the trip from 1 to 2: 1 hr25 km16o24 km7 kmDon’t worry about this notation for this test Speed = 31 km/hVelocity = 25 km/h at 16o NEIf an object STARTS & STOPS at the same point, the velocity is ZERO! (since the displacement is zero)
25x-t graphst (sec)x (m)t t t3x2x1x3BCDAConstant speed (Constant + velocity, or constant velocity in the + direction)Slow down, speed up, slow down, speed up2 moments where the object is “at rest” (for a moment)
26How to get the position (x) at a certain time (t) off an x-t graph x(m)t (s)302010Example:What is the position at t = 30 seconds?24mGo over to t = 30.Find the pt on the curve.Find the x value for this time.
27How to calculate the displacement between two times on an x-t graph x(m)t (s)302010Example:What is the displacement from t = 10 to t = 40?17 mFind x1Find x210 mUse D x = x2 - x1 = + 7 m
28How to find the distance traveled between two times on an x-t graph. x(m)t (s)302010Example:What is the distance traveled from t = 10 to t = 40?17 m10 mFind the distance traveled in the + direction.Find the distance traveled in the - direction.Add them together. (27 m)
29Understand the difference between velocity and speed on an x-t graph. x(m)t (s)302010Example:What is the average speed from t = 10 to t = 40 seconds?17 m10 mdist10-40 = 27 m(previous slide)Avg. Speed = dist/ Dt= 27m / 30 sec= 0.9 m/s
30Understand the difference between velocity and speed on an x-t graph. x(m)t (s)302010Example:What is the average velocity from t = 10 to t = 40 seconds?Dx10-40 = + 7 m (previous slide)Avg. Velocity = slope= Dx/ Dt= + 7 / 30 sec= m/s
31Will 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.
32Negative Average Velocity? x(m)t (s)302010Example:What is the average velocity from t = 20 to t = 40 seconds?Avg. vel. = slope = rise/run = -7 m / 20= -.35 m/sSince the objects displacement is in the NEGATIVE direction, so is its average velocity.
33Open to in your Unit 1 packet 1 -10 m2)3)4)avg velocity = slope = -15m / 6sec = -2.5 m/ss = |v| = 2.5 m/sAt rest at t = 0 and t = 12 sec