Motion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.

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1 Motion ccelertion Prt : Constnt ccelertion ccelertion ccelertion ccelertion is the rte of chnge of elocity. = - o t = Δ Δt ccelertion = = - o t chnge of elocity elpsed time ccelertion is ector, lthough in one-dimensionl motion we only need the sign. Since only constnt ccelertion will be considered in this course, there is no need to differentite between erge nd instntneous ccelertion. Units for ccelertion ccelertion is the rte of chnge of. Units for ccelertion You cn derie the units by substituting the correct units into the right hnd side of these equtions. = Δ Δt m/s s = m/s C D displcement distnce speed elocity Ms. Leine

2 The unit for elocity is: 3 The metric unit for ccelertion is: m m m/s m/s C m/s D ft/s C m/s D ft/s 4 horse gllops with constnt ccelertion of 3m/s. Which sttement below is true? 5 Your elocity chnges from 60 m/s to the right to 00 m/s to the right in 0 s; wht is your erge ccelertion? C D The horse's elocity doesn't chnge. The horse moes 3m eery second. The horse's elocity increses 3m eery second. The horse's elocity increses 3m/s eery second. 6 Your elocity chnges from 60 m/s to the right to 0 m/s to the right in 0 s; wht is your erge ccelertion? 7 Your elocity chnges from 50 m/s to the left to 0 m/s to the right in 5 s; wht is your erge ccelertion? Ms. Leine

3 8 Your elocity chnges from 90 m/s to the right to 0 m/s to the right in 5.0 s; wht is your erge ccelertion? Kinemtics Eqution Return to Tble of Contents Motion t Constnt ccelertion = Δ Δt but since "Δ" mens chnge 9 Strting from rest, you ccelerte t 4.0 m/s for 6.0s. Wht is your finl elocity? Δ = - o nd = - o t t = - o - o = t Δt = t - to if we lwys let to = 0, Δt = t Soling for "" = o + t This eqution tells us how n object's elocity chnges s function of time. 0 Strting from rest, you ccelerte t 8.0 m/s for 9.0s. Wht is your finl elocity? You he n initil elocity of 5.0 m/s. You then eperience n ccelertion of -.5 m/s for 4.0s; wht is your finl elocity? Ms. Leine 3

4 You he n initil elocity of -3.0 m/s. You then eperience n ccelertion of.5 m/s for 9.0s; wht is your finl elocity? 3 How much time does it tke to ccelerte from n initil elocity of 0m/s to finl elocity of 00m/s if your ccelertion is.5 m/s? 4 How much time does it tke to come to rest if your initil elocity is 5.0 m/s nd your ccelertion is -.0 m/s? 5 n object ccelertes t rte of 3 m/s for 6 s until it reches elocity of 0 m/s. Wht ws its initil elocity? 6 n object ccelertes t rte of.5 m/s for 4 s until it reches elocity of 0 m/s. Wht ws its initil elocity? Grphing Motion t Constnt ccelertion In physics there is nother pproch in ddition to lgebric which is clled grphicl nlysis. The formul = 0 + t cn be interpreted by the grph. We just need to recll our memory from mth clsses where we lredy sw similr formul y = m + b. From these two formuls we cn some nlogies: y (dependent rible of ), 0 b (intersection with erticl is), t (independent rible), m ( slope of the grph- the rtio between rise nd run Δy/Δ). Ms. Leine 4

5 Motion t Constnt ccelertion elow we cn find the geometric eplntion to the ccelertion =Δ/Δt. If slope is equl to: m = Δy/Δ Motion t Constnt ccelertion The grph on the right hs slope of Δ/Δt, which is equl to ccelertion. Therefore, the slope of elocity s. time grph is equl to ccelertion. Then consider grph with elocity on the y-is nd time on the -is. Wht is the slope for the grph on the right? (slope) y =Δy/Δ (slope of elocity s. time) =Δ/Δt 7 The elocity s function of time is presented by the grph. Wht is the ccelertion? 8 The elocity s function of time is presented by the grph. Find the ccelertion. Motion t Constnt ccelertion The ccelertion grph s function of time cn be used to find the elocity of moing object. When the ccelertion is constnt the elocity is chnging by the sme mount ech second. This cn be shown on the grph s stright horizontl line. In order to find the chnge in elocity for certin limit of time we need to clculte the re under the ccelertion line tht is limited by the time interl. 9 The following grph shows ccelertion s function of time of moing object. Wht is the chnge in elocity during first 0 seconds? Ms. Leine 5

6 Free Fll Free Fll: ccelertion Due to Grity ll unsupported objects fll towrds Erth with the sme ccelertion. We cll this ccelertion the "ccelertion due to grity" nd it is denoted by g. g = 9.8 m/s Keep in mind, LL objects ccelerte towrds the erth t the sme rte. g is constnt! Return to Tble of Contents Click here to wtch Glileo's fmous eperiment performed on the moon It Wht stops hppens momentrily. t the top? = 0 It stops momentrily. = 0 It slows down. Wht hppens when it (negtie ccelertion) goes up? It Wht speeds hppens up when it (negtie goes down? ccelertion) It slows down. (negtie ccelertion) It speeds up. (negtie ccelertion) n object is thrown upwrd with initil elocity, o It returns Wht hppens with its when it originl lnds? elocity. n object is thrown upwrd with initil elocity, o It returns with its originl elocity. On the wy up: 0 t = 3 s t = s t = s t = 0 s On the wy down: 0 t = 0 s t = s t = s t = 3 s For ny object thrown stright up into the ir, this is wht the elocity s. time grph looks like. (m/s) n object is thrown upwrd with initil elocity, o It stops momentrily. = 0 It returns with its originl elocity but in the opposite direction. Ms. Leine 6

7 Lb Phyiscs elocity is constnt C elocity is decresing D ccelertion is decresing rock flls off cliff nd hits the ground 5 seconds lter. Wht elocity did it hit the ground with? 3 bll is thrown down off bridge with elocity of 5 m/s. Wht is its elocity seconds lter? 5 rocket is fired stright up from the ground. It returns to the ground 0 seconds lter. Wht ws its lunch speed? ccelertion is constnt n rrow is fired into the ir nd it reches its highest point 3 seconds lter. Wht ws its elocity when it ws fired? 4 Ms. Leine n corn flls from n ok tree. You note tht it tkes.5 seconds to hit the ground. How fst ws it going when it hit the ground? bll is dropped from rest nd flls (do not consider ir resistnce). Which is true bout its motion? 0 7

8 6 n object ccelertes from rest, with constnt ccelertion of 8.4 m/s, wht will its elocity be fter s? Grphing Return to Tble of Contents Velocity s. Time Grphs Similrly, the sme pproch cn be used to crete elocity s. time grph. elocity ersus time grph differs by hing the elocity on the erticl is. (m/s) Strting t the position, 0 = 4 m, you trel t constnt elocity of + m/s for 6s. b. Drw the Position ersus Time for your trel during this time. Drg nd drop the dt points on the grph in order to construct the s t pttern! elocity ersus time grph shows describes n objects elocity, it's displcement, nd ccelertion Drw line of best fit to obsere the pttern. Strting t the position, 0 = 4 m, you trel t constnt elocity of + m/s for 6s. c. Drw the Velocity ersus Time grph for your trip. Drg nd drop the dt points on the grph in order to construct the s t pttern! (m/s) Strting t the position, 0 = 0 m, you trel t constnt elocity of -m/s for 6s. b. Drw the Position ersus Time for your trel during this time. Drg nd drop the dt points on the grph in order to construct the s t pttern! Drw line of best fit to obsere the pttern. Drw line of best fit to obsere the pttern Ms. Leine 8

9 nlyzing Position s Time Grphs nlyzing Position s Time Grphs Recll erlier in this unit tht slope ws used to describe motion. positie slope is positie elocity, negtie slope is negtie elocity, nd slope of zero mens zero elocity. The slope in position s. time grph is Δ/Δt, which is equl to elocity. Δt Δ = Δ/Δt positie slope > 0 negtie slope < 0 zero slope = 0 Therefore, slope is equl to elocity on position s. time grph. positie elocity mens moing in the positie direction, negtie elocity mens moing in the negtie direction, nd zero elocity mens not moing t ll. The position ersus time grph, below, describes the motion of three different crs moing long the -is. b. Clculte the elocity of ech of the crs. Position The elocity s time grph, below, describes the motion of n object moing long the -is. 4 (m/s) Describe in words wht is hppening to the speed during the following interls. ) 0s to s b) s to 3s c) 3s to 4 sec d) 4s to 5s e) 5s to 6s 73 The elocity s time grph, below, describes the motion of n object moing long the -is. 4 (m/s) Determine the erge speed during the following interls. ) 0s to s b) s to 3s c) 3s to 4 sec d) 4s to 5s e) 5s to 6s f) 4s to 6s Summry Kinemtics is the description of how objects moe with respect to defined reference frme. Displcement is the chnge in position of n object. erge elocity is the displcement diided by the time. erge ccelertion is the chnge in elocity diided by the time. Ms. Leine 9