+v Today: Graphing v (miles per hour ) 9 8 7 6 5 4 - - Time Noe: I hope his joke will be funnier (or a leas make you roll your eyes and say ugh ) afer class.
Do yourself a favor! Prof Sarah s fail-safe learning plan Try he homework yourself. Ge ogeher and solve he problems or similar ones suggesed in lecure. Try he homework again. (you ll learn beer, and anyways, work mus be your own!) Use Facebook o sar/find a sudy group! hps://www.facebook.com/ groups/664979549/
Clickers will be used in class almos every day afer his! If one day you forge your clicker, please wrie clicker answers on a piece of paper. If you have a borderline grade I will look a hese (oherwise I will no)!
Today s opics Graphing. Basic erms and conceps Displacemen Velociy Acceleraion Insananeous versus average v and a.
Common Graphing Lingo Noe: You will do hands on graphing work in lab v = v + a
Common Graphing Lingo y/verical axis: Dependen variable The hing you measure. The value of his variable depends on he oher variable. Noe: You will do hands on graphing work in lab v = v + a Verical axis = locaion (m) velociy (m/s) acceleraion (m/s )
Common Graphing Lingo y/verical axis: Dependen variable The hing you measure. The value of his variable depends on he oher variable. Noe: You will do hands on graphing work in lab v = v + a Verical axis = locaion (m) velociy (m/s) acceleraion (m/s ) x/horizonal axis: Independen variable We can change his variable o see how i effecs he oher. Horizonal axis =
How posiion changes as a funcion of ime +x x (m) 6 5 4-4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4-4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4-4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4 - consan +v 4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4 - consan +v 4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4 - v = consan +v 4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4 - v = consan +v 4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4 - v = consan -v consan +v 4 5 6 7 8 9 4 5 x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4-4 5 6 7 8 9 4 5 / = consan +v = no v \ = consan -v x (meers)
How posiion changes as a funcion of ime +x x (m) 6 5 4-4 5 6 7 8 9 4 5 / = consan +v = no v \ = consan -v x (meers)
Calculaing Average Velociy (on an x vs plo) +x x (m) 6 5 4 - B A Δ Δx 4 5 6 7 8 9 4 5 v Δx Δ Slope of line beween wo poins on he curve: average velociy
Calculaing Average Velociy (on an x vs plo) +x x (m) 6 5 4 - B A 4 5 6 7 8 9 4 5 Δx 4m - m m v = = = = m/s Δ 4s - s s
Calculaing Average Velociy (on an x vs plo) +x x (m) 6 5 4 - B A Δ Δx 4 5 6 7 8 9 4 5 Δx 4m - m m v = = = = m/s Δ 4s - s s
Calculaing Average Velociy (on an x vs plo) +x Q x (m) Wha s he car doing? A. Approaches wall slowly, hen reverses rapidly. B. Goes slowly away from wall, hen reurns fas. C. Speeds away from wall, hen reurns slowly. +x D. Speeds oward he wall, hen backs away slowly. E. Tailgaing
Calculaing Average Velociy (on an x vs plo) +x Q Δx Wha s he car doing? x (m) Δ Δx Δ A. Approaches wall slowly, hen reverses rapidly. B. Goes slowly away from wall, hen reurns fas. C. Speeds away from wall, hen reurns slowly. +x D. Speeds oward he wall, hen backs away slowly. E. Tailgaing
Insananeous vs. Average Velociy Average velociy: velociy averaged over a ime inerval. +x x (m) 6 5 4 4 5 6 7 8 9 4 5
Insananeous vs. Average Velociy Average velociy: velociy averaged over a ime inerval. +x x (m) 6 5 4 Δ Δx 4 5 6 7 8 9 4 5
Insananeous vs. Average Velociy Average velociy: velociy averaged over a ime inerval. +x x (m) 6 5 4 Δ Δx Average velociy beween and seconds = slope of line beween hese poins on he curve 4 5 6 7 8 9 4 5
Insananeous vs. Average Velociy Average velociy: velociy averaged over a ime inerval. +x x (m) 6 5 4 Δ Δx 4 5 6 7 8 9 4 5
Insananeous vs. Average Velociy Average velociy: velociy averaged over a ime inerval. +x x (m) 6 5 4 4 5 6 7 8 9 4 5 Insananeous velociy: velociy a one insan
Insananeous vs. Average Velociy Average velociy: velociy averaged over a ime inerval. +x x (m) 6 5 4 Δ Δx Insananeous velociy a 8 seconds = slope of line angenial o ha poin on he curve 4 5 6 7 8 9 4 5 Insananeous velociy: velociy a one insan
Q
Q
Q
Q
Q
Q
Q
Q A CURVE in x vs means CHANGE IN v and hence ACCELERATION.
Velociy vs. Time +v v (m/s) 6 5 4-4 5 6 7 8 9 4 5
Velociy vs. Time +v v (m/s) 6 5 4-4 5 6 7 8 9 4 5 FASTER SLOWER SLOWER FASTER Velociy vecor is posiive a res (v = ) Velociy vecor is negaive
Velociy vs. Time +v v (m/s) 6 5 4-4 5 6 7 8 9 4 5 / = increasing velociy = consan velociy \ = decreasing velociy
Velociy vs. Time +v v (m/s) 6 5 4-4 5 6 7 8 9 4 5 Wha does he x vs graph look like? A. B. C. D. Q
Calculaing Average Acceleraion (on a v vs plo) +v v (m/s) 6 5 4 - A B 4 5 6 7 8 9 4 5 Δ Δv C a Δv Δ Slope of line beween wo poins on he curve: average acceleraion
Calculaing Average Acceleraion (on a v vs plo) +v v (m/s) 6 5 4 - A B 4 5 6 7 8 9 4 5 Δ Δv C a Δv Δ Slope of line beween wo poins on he curve: average acceleraion
Calculaing Average Acceleraion (on v vs plo) +v v (m/s) 6 5 4 - A B 4 5 6 7 8 9 4 5 Δ Δv C Slope of line angenial o one poin on he curve: insananeous acceleraion
Velociy vs. Time +v v (m/s) 6 5 4-4 5 6 7 8 9 4 5 / = velociy more and more posiive [consan +a] = consan velociy [no a] \ = velociy more and more negaive [consan -a]
+v v (m/s) 6 5 4 4 5 6 7 8 9 4 5 Wha are he signs of he velociy vecors, and acceleraion vecor, beween and seconds? Q4 A. v s -, a - B. v s +, a - C. v s -, a + D. v s +, a + E. Boh are zero.
+v v (m/s) 6 5 4 4 5 6 7 8 9 4 5 Wha are he signs of he velociy vecors, and acceleraion vecor, beween and seconds? Q4 A. v s -, a - B. v s +, a - C. v s -, a + D. v s +, a + E. Boh are zero.
Acceleraion vs. Time +a a (m/s ) - - - 4 5 6 7 8 9 4 5 In his class, acceleraion will always be horizonal line segmens (consan accel over se periods)
Acceleraion vs. Time +a a (m/s ) - - - 4 5 6 7 8 9 4 5 Posiive acceleraion NO CHANGE in velociy! Negaive acceleraion
Acceleraion vs. Time +a a (m/s ) - - - 4 5 6 7 8 9 4 5 Posiive acceleraion NO CHANGE in velociy! Negaive acceleraion You can infer he sign of v or x jus by knowing he sign of acceleraion (i migh ac wih or agains he movemen)! Bu you CAN know sign of acceleraion from velociy and posiion informaion.
An objec is speeding up uniformly in he posiive direcion. Which of he following represens his moion? A. +a B. +a -a -a C. +a D. +a -a -a Q5
An objec is speeding up uniformly in he negaive direcion. Which of he following represens his moion? A. +a B. +a -a -a C. +a D. +a -a -a Q6
Las Thing: Moion Vecor Diagrams! Draw wo horizonal lines on your paper
Las Thing: Moion Vecor Diagrams! Draw wo horizonal lines on your paper walking
Las Thing: Moion Vecor Diagrams! Draw wo horizonal lines on your paper walking running
Moion Vecor Diagrams
Moion Vecor Diagrams a
Moion Vecor Diagrams av
This objec moves along he x-direcion wih consan acceleraion. Saring wih, he dos,,, show he posiion of he objec a equal ime inervals. 4 5 x = x Which of he following v- graphs bes maches he moion shown in he moion diagram? +v +v +v +v +v A. B. C. D. E.
PRACTICE building your inuiion! All of hese ses are valid. Why? +x +x +x +v +v +v +a +a +a Moion diagrams 4 +x 5 6 7 8 4 +x 7 6 5,,,4 +x
Wha you learn from graphs? Type of graph Posiion vs Time Velociy vs Time Slope gives: Velociy Acceleraion Change of physical direcion A maximum or minimum When curve crosses axis Acceleraion vs Time --- Can deermine
Wha you learn from graphs? Type of graph Posiion vs Time Velociy vs Time Slope gives: Velociy Acceleraion Change of physical direcion A maximum or minimum When curve crosses axis Acceleraion vs Time --- Can deermine Inegraion (calculus) les you find he area under a curve, bu we won be doing ha