Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh line.
Disance The oal lengh of he pah raveled by an objec is called disance. How far have you walked? is a ypical disance quesion. The SI uni of disance is he meer (m).
Displacemen ( x) The change in he posiion of a paricle is called displacemen. is a Greek leer used o represen he words change in. x herefore means change in x. I is always calculaed by final value minus iniial value. How far are you from home? is a ypical displacemen quesion. The SI uni for displacemen is he meer. Calculaion of displacemen: x x x f i
Disance vs Displacemen B 100 m displacemen 50 m A disance A picure can help you disinguish beween disance and displacemen.
Quesions Does he odomeer in your car measure disance or displacemen? Can you hink of a circumsance in which i measures boh disance and displacemen?
Pracice Problem: Two ennis players approach he ne o congraulae one anoher afer a game. a) Find he disance and displacemen of player A. b) Repea for player B. A B 5 m 2 m
Pracice Problem: If x is he displacemen of a paricle, and d is he disance he paricle raveled during ha displacemen, which of he following is always a rue saemen? a) d = x b) d < x c) d > x d) d > x e) d < x
Pracice Problem A paricle moves from x = 1.0 meer o x = -1.0 meer. Wha is he disance d raveled by he paricle? Wha is he displacemen of he paricle?
Pracice Problem: You are driving a car on a circular rack of diameer 40 meers. Afer you have driven around 2 ½ imes, how far have you driven, and wha is your displacemen?
Average Speed Average speed describes how fas a paricle is moving. The equaion is: s ave d where: Average speed is s ave = average speed always a posiive d = disance number. = elapsed ime The SI uni of speed is he m/s
Average Velociy Average velociy describes how fas he displacemen is changing. The equaion is: v ave Average velociy where: is + or v ave = average velociy depending on x = displacemen direcion. = elapsed ime The SI uni of velociy is he m/s. x
Pracice Problem: How long will i ake he sound of he saring gun o reach he ears of he spriners if he sarer is saioned a he finish line for a 100 m race? Assume ha sound has a speed of abou 340 m/s.
Pracice Problem: You drive in a sraigh line a 10 m/s for 1.0 km, and hen you drive in a sraigh line a 20 m/s for anoher 1.0 km. Wha is your average velociy?
Graphical Problem x A B x v ave = x/ Wha physical feaure of he graph gives he consan velociy from A o B?
Graphical Problem: Deermine he average velociy from he graph. x (m)
Graphical Problem: Deermine he average velociy beween 1 and 4 seconds.
Graphical Problem x Describe he moion of his paricle.
Graphical Problem x Describe he moion of his paricle.
Draw Graphs for Saionary Paricles x x Posiion vs ime Posiion vs ime
Draw Graphs for Consan Non-zero Velociy x x x Posiion vs ime Posiion vs ime Posiion vs ime
Draw Graphs for Consan Non-zero Velociy v v v
Graphical Review Problem x Describe he moion of hese wo paricles.
Graphical Problem v Describe he moion of hese wo paricle.
Graphical Problem x Wha kind of moion does his graph represen?
Graphical Problem x B x A v ave = x/ Can you deermine average velociy from he ime a poin A o he ime a poin B from his graph?
Insananeous Velociy The velociy a a single insan in ime. If he velociy is uniform, or consan, he insananeous velociy is he same as he average velociy. If he velociy is no consan, han he insananeous velociy is no he same as he average velociy, and we mus carefully disinguish beween he wo.
Insananeous Velociy x v ins = x/ B x Draw a angen line o he curve a B. The slope of his line gives he insananeous velociy a ha specific ime.
Pracice Problem: Deermine he insananeous velociy a 1.0 second.
Posiion vs Time Graphs Paricles moving wih no acceleraion (consan velociy) have graphs of posiion vs ime wih one slope. The velociy is no changing since he slope is consan. Posiion vs ime graphs for paricles moving wih consan acceleraion look parabolic. The insananeous slope is changing. In his graph i is increasing, and he paricle is speeding up.
Acceleraion (a) Any change in velociy over a period of ime is called acceleraion. The sign (+ or -) of acceleraion indicaes is direcion. Acceleraion can be speeding up slowing down urning
Quesions If acceleraion is zero, wha does his mean abou he moion of an objec? Is i possible for a racecar circling a rack o have zero acceleraion?
Uniform (Consan) Acceleraion In Physics B, we will generally assume ha acceleraion is consan. Wih his assumpion we are free o use his equaion: a v The SI uni of acceleraion is he m/s 2.
Acceleraion in 1-D Moion has a sign! If he sign of he velociy and he sign of he acceleraion is he same, he objec speeds up. If he sign of he velociy and he sign of he acceleraion are differen, he objec slows down.
Pracice Problem: A 747 airliner reaches is akeoff speed of 180 mph in 30 seconds. Wha is is average acceleraion?
Pracice Problem: A horse is running wih an iniial velociy of 11 m/s, and begins o accelerae a 1.81 m/s 2. How long does i ake he horse o sop?
Uniformly Acceleraing Objecs You see he car move faser and faser. This is a form of acceleraion. The posiion vs ime graph for he acceleraing car reflecs he bigger and bigger x values. The velociy vs ime graph reflecs he increasing velociy.
Graphical Problem v (m/s) 0.50 (s) Demonsrae he moion of his paricle. Is i acceleraing?
Graphical Problem v Demonsrae he moion of his paricle. Is i acceleraing?
Graphical Problem v A B v a = v/ Wha physical feaure of he graph gives he acceleraion?
Pracice Problem: Deermine he acceleraion from he graph.
Pracice Problem: Deermine he displacemen of he objec from 0 o 4 seconds. How would you describe he moion of his paricle?
Describe he moion This objec is moving in he posiive direcion and acceleraing in he posiive direcion (speeding up). This objec is moving in he negaive direcion and acceleraing in he negaive direcion (speeding up). This objec is moving in he negaive direcion and acceleraing in he posiive direcion (slowing down).
Draw Graphs for Saionary Paricles x v a Posiion vs ime Velociy vs ime Acceleraion vs ime
Draw Graphs for Consan Non-zero Velociy x v a Posiion vs ime Velociy vs ime Acceleraion vs ime
Draw Graphs for Consan Non-zero Acceleraion x v a Posiion vs ime Velociy vs ime Acceleraion vs ime
Kinemaic Equaions v v a o o 2 2 1 2 x x v a v v 2 a( x) 0 o 2
Pracice Problem: Wha mus a paricular Olympic spriner s acceleraion be if he is able o aain his maximum speed in ½ of a second?
Pracice Problem: A plane is flying in a norhwes direcion when i lands, ouching he end of he runway wih a speed of 130 m/s. If he runway is 1.0 km long, wha mus he acceleraion of he plane be if i is o sop while leaving ¼ of he runway remaining as a safey margin?
Pracice Problem: On a ride called he Deonaor a Worlds of Fun in Kansas Ciy, passengers accelerae sraigh downward from 0 o 20 m/s in 1.0 second. a) Wha is he average acceleraion of he passengers on his ride? b) How fas would hey be going if hey acceleraed for an addiional second a his rae?
Pracice Problem -- coninued c) Skech approximae x-vs-, v-vs- and a-vs- graphs for his ride.
Pracice Problem: Air bags are designed o deploy in 10 ms. Esimae he acceleraion of he fron surface of he bag as i expands. Express your answer in erms of he acceleraion of graviy g.
Pracice Problem: You are driving hrough own a 12.0 m/s when suddenly a ball rolls ou in fron of you. You apply he brakes and decelerae a 3.5 m/s 2. a) How far do you ravel before sopping? b) When you have raveled only half he sopping disance, wha is your speed?
Pracice Problem -- coninued c) How long does i ake you o sop? d) Draw x vs, v vs, and a vs graphs for his.
Free Fall Free fall is a erm we use o indicae ha an objec is falling under he influence of graviy, wih graviy being he only force on he objec. Graviy acceleraes he objec oward he earh he enire ime i rises, and he enire ime i falls. The acceleraion due o graviy near he surface of he earh has a magniude of 9.8 m/s 2. The direcion of his acceleraion is DOWN. Air resisance is ignored. Le s see some demos!
Pracice Problem: You drop a ball from res off a 120 m high cliff. Assuming air resisance is negligible, a) how long is he ball in he air? b) wha is he ball s speed and velociy when i srikes he ground a he base of he cliff? c) skech approximae x-vs-, v-vs-, a-vs- graphs for his siuaion.
Symmery in Free Fall When somehing is hrown sraigh upward under he influence of graviy, and hen reurns o he hrower, his is very symmeric. The objec spends half is ime raveling up; half raveling down. Velociy when i reurns o he ground is he opposie of he velociy i was hrown upward wih. Acceleraion is 9.8 m/s 2 and direced DOWN he enire ime he objec is in he air!
Pracice Problem: You hrow a ball sraigh upward ino he air wih a velociy of 20.0 m/s, and you cach he ball some ime laer. a) How long is he ball in he air? b) How high does he ball go?
Pracice Problem -- coninued c) Wha is he ball s velociy when you cach i? d) Skech approximae x-vs-, v-vs-, a-vs- graphs for his siuaion.
Pinewood Derby x(m) 0 2.3 9.2 20.7 36.8 57.5 (s) 0 1.0 2.0 3.0 4.0 5.0 On your graph paper, do he following. a) Draw a posiion vs ime graph for he car. b) Draw angen lines a four differen poins on he curve o deermine he insananeous velociy a all four poins. c) On a separae graph, draw a velociy vs ime graph using he insananeous velociies you obained in he sep above. d)from your velociy vs ime graph, deermine he acceleraion of he car.