Graphical Analysis of motion in _________________ one direction Distance and displacement. 20 d (m) 10 t (s) 5 10 15 What is the total distance moved? 20 + 10 = 30 m What is the resultant displacement? +10 m Find the average speed in the 0-5 s interval. Repeat for 5-10 s and 10-15 s. 20 m 5 s 0 m , 10 m 5 s 5 s

II. Uniform motion – ____________ is constant velocity A. Graph of d vs. t speed v slope =_____ d/t = ________ slope =______________ constant speed = _______________ constant A d same t ________d in each _____ What would the graph of a slower object look like? B Slower  less slope t 1 2 How much slower is B? half the speed of A

B. Graph of speed __________ for uniform motion v vs. t slope =______ Dv/t slope =______ a v A slope =________________ constant = 0 a =_________ B What about B? t B is slower  lower What does the area shown represent? speed x time distance area = L x W = _____________ =_____________ [m/s] [s] [m] units: ______ x ______ = _________

a C. Graph of a vs. t for uniform motion a = 0 a = 0 t How would you graph B? Same. In review: for __________________ Motion: Uniform A d v a A B B a = 0 t t t

Ex: tape timers timer marks the tape at constant ________ intervals time cart pulls tape ________________ through timer paper tape constant v timer As car moves, describe pattern of marks on tape. _____________ spaced b/c car moves the __________ d between each mark. Equally same How would tape look if car was twice as fast?

III. Non-uniform motion: ___________________ acceleration constant (non-0) A. Graph of d vs. t for object beginning at rest slope of tangent is the ______________________ d instantaneous v initial ________speed vi = ___  __________________ 2 slope = 0 at t = 0 increases The slope ___________ 1 b/c speed v ___________ increases t more dashed lines are__________ Object covers ________ d in each________________ tangents t interval

Graph of speed v vs. t for __________________ acceleration a beginning _______________ . constant (non-0) at rest slope =________ Dv/t v accel. a = __________ constant ≠ 0 slope = _______________ t a = ______________ constant What does the area shown represent? distance area = (1/2) bh = (½) ______________=__________ time x speed [s] [m/s] [m] units : ______ x ______ = ______

C. Graph of a vs. t for constant a a a = constant t In review: For _________________________acceleration constant, non-zero v d a t t t

Timer tape for ___________________ constant a Ex: Timer tape for ___________________ constant a paper tape cart constant a timer As car moves, describe pattern of marks on tape. Un-equally more _______________ spaced b/c car moves _________ distance d between each mark. How would tape look if car had more acceleration?

Compare ____________ to ________________motion: uniform accelerated Compare ____________ to ________________motion: d v a Uniform area = d t t t slope = v slope = a v a d area = d Accel. t t t

What is the total distance traveled? d (m) Ex. Answer the questions based on the graph at right. 4 t (s) 2 4 6 -8 What is the total distance traveled? 8 + 8 + 4 = 20 m What is the resultant displacement? +4 m Find the average speed in the first 2 s. Find the average speed over the entire 6 s. Find the average velocity over the entire 6 s. 8 m 2 s 20 m 6 s +4 m 6 s

Find vavg, d, and a in regions A, B and C. Ex: The graph below describes a UFO moving in a straight line. t (s) v (m/s) 4.0 8.0 12 20. 40. A B C Find vavg, d, and a in regions A, B and C.

In A: v = vi + vf 2 = (20. m/s + 40. m/s) / 2 = 30. m/s v = d/t d = v t = (30. m/s)(4.0 s) = 120 m = area in A a = Δv/t = (vf – vi)/t = (40. m/s – 20. m/s) / 4.0 s = 5.0 m/s/ s = 5.0 m/s2

In B: v = vi + vf 2 = (40. + 40.) / 2 = 40. m/s v = d/t d = v t = (40. m/s)(6.0 s) = 240 m = area in B a = Δv/t = (vf – vi)/t = (40. m/s – 40. m/s) / 6.0 s = 0

In C: v = (40. + 0) / 2 = 20. m/s d = v t = (20. m/s)(2.0 s) = 40. m = area in ΔC: ½bh a = Δv/t = (vf – vi)/t = (0 m/s – 40. m/s) / 2.0 s = -20. m/s2

v (m/s) 20. 40. A B C 120 m 240 m 40 m 8.0 12 t (s) 4.0 = v Which area, A, B or C, is uniform motion? area = d a= slope Which area, A, B or C, is the acceleration constant, but not zero? Where is the acceleration NOT constant?