SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton the ccelerton t ny prtculr ntnt. l. t 0 t dt The lope o curve on velocty-te grph repreent the ccelerton. The re under the curve on n ccelerton-te grph repreent the chnge n velocty. There re 5 vrble nvolved n the thetcl nly o oton wth contnt ccelerton:, v, v, d, t There re 5 equton tht llow you to olve oton proble wth contnt ccelerton: d x x 0 v v t d vt t v v d d v v t d v t t You cn olve ll proble you ue both equton ultneouly: v v t d vt t Accelerton the rte t whch velocty chnge. Jut we dd or velocty, we cn dene verge ccelerton over n ntervl or ntntneou ccelerton t pecc oent n te. Averge ccelerton: ve v t v v t Intntneou ccelerton: v l t 0 t dv dt I you re gven grph o velocty veru te, the verge ccelerton over n ntervl jut the lope o the lne connectng the two end o the ntervl (ecnt lne), nd the ntntneou ccelerton the lpe o the tngent lne drwn to the grph t the gven te. The net re under the velocty veru te grph jut the dplceent, the re totl dtnce trvelled. d. The bolute vlue o
SPH3UW Unt. Accelerton n One Denon Pge o 9 Note o Cuton: Keep n nd tht negtve ccelerton doe not necerly en tht n object lowng down. I the ccelerton negtve, nd the velocty negtve, the object peedng up! Exple A cr peed up wth n verge ccelerton wth gntude o 6., deterne t velocty ter.7 t ntl w 3 E.
SPH3UW Unt. Accelerton n One Denon Pge 3 o 9 Soluton: Fro ve v v v t t The nl velocty 4 E Exple Snce ccelerton peedng up, t n the e drecton velocty [E].. v 3 E 6. E.7 0.54 3 0.54 E 3 E v v 4.54 E 4 E E v E gncnt dgt. Fro the ollowng velocty v te grph: ) generte the correpondng poton-te grph b) generte the correpondng ccelerton-te grph c) deterne the ntntneou velocty t t= econd nd t=4 econd
SPH3UW Unt. Accelerton n One Denon Pge 4 o 9 ) b)
SPH3UW Unt. Accelerton n One Denon Pge 5 o 9 c) The ntntneou velocty t t= 6 / The ntntneou velocty t t=4 9 / Thee 5 equton ut be eorzed nd prctced wth nee. Equton or oton wth Contnt Accelerton Equton Mng Quntty * v v0 t x x0 * x x0 v0t t v 0 0 v v x x t x x0 v0 vt x x vt t 0 0 v The two equton wth n * cn be ued to olve ny proble. You olve both equton ultneouly nd cobne. Exple Obervng trc lowdown, you brke your cr ro peed o 00 k/h to peed o 80.0 k/h durng dplceent o 88.0, t contnt ccelerton. ) Wht tht ccelerton? b) How uch te requred or the gven decree n peed?
SPH3UW Unt. Accelerton n One Denon Pge 6 o 9 Soluton: We re gven: x x0 88.0 k h 000 v0 00 7.8 h 3600 k t? ) Method? Ung v v0 t nd k h 000 v v 80.0. h 3600 k x x0 v0t t v v t. 7.8 t 5.6 t 0 nd ubttute nto x x0 v0t t 5.6 5.6 88.0 7.8 55.68 5.68 88.0 40 88.0 40 88.0.59 Thu the ccelerton (n the oppote drecton velocty) -.59 /.
SPH3UW Unt. Accelerton n One Denon Pge 7 o 9 Method Snce we wnt the ccelerton nd the ng vrble t, thereore we cn ply ue v v x x 0 0 v v x x 0 0. 7.8 88.0.59 b) We hve ll pece o norton or the equton o oton o we cn ue ny equton. Let ue the eet orul: v v t 0.. 7.8.59 t t 3.5 Exple: The velocty o prtcle ovng long the x x vre n te ccordng to the expreon vx 50 4t /,,where t n econd. ) Fnd the verge ccelerton n the te ntervl t =0 to t=.0 b) Deterne the ccelerton t t =.0. Soluton: ) v v 50 4 0 50 50 4 46 x v 46 50 v 4 t t 0 The negtve gn rend u tht nce nl velocty ller thn ntl, t lowng down.
SPH3UW Unt. Accelerton n One Denon Pge 8 o 9 b) We recll tht x v l t 0 t v 50 4t We lo note tht 50 4 50 4 8 4 v t t t t t Cobnng: x v l t 0 t v v l t 0 t t t 0 50 4t 8t 4 t 50 4t l t 0 t 8t 4 l t 0 t l8 4t 8 t Becue the velocty o the prtcle potve nd the ccelerton negtve, the prtcle lowng down.
SPH3UW Unt. Accelerton n One Denon Pge 9 o 9 Extr Note nd Coent