Solving Equations. PHYSICS Solving Equations. solving equations NOTES. Solving for a Variable. The Rules. The Rules. Grade:«grade»

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1 olving equaion NOTES New Jerey ener for Teaching an Learning Progreive Science Iniiaive Thi maerial i mae freely available a an i inene for he non commercial ue of uen an eacher. Thee maerial may no be ue for any commercial purpoe wihou he wrien permiion of he owner. NJTL mainain i webie for he convenience of eacher who wih o make heir work available o oher eacher, paricipae in a virual profeional learning communiy, an/or provie acce o coure maerial o paren, uen an oher. PHYSIS Solving Equaion lick o go o webie: Solving Equaion Solving for a Variable Our goal i o be able o olve any equaion for any variable ha appear in i. Le' look a a imple equaion fir. Grae:«grae» Subjec:Honor Phyic ae:«ae» The variable in hi equaion are, an. Solving for a variable mean having i alone on he lef ie. Thi equaion i currenly olve for "". The Rule The Rule Like in any game here are a few rule. Le' olve hi equaion for "" 1. To "uno" a mahemaical operaion, you mu o he oppoie. 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. 3. If here i more han one operaion going on, you mu uno hem in he oppoie orer in which you woul o hem, he oppoie of he "orer of operaion." Tha mean ha when we're one we'll have alone on he lef ie of he equaion. 4. You can alway wich he lef an righ ie of an equaion. 1

2 olving equaion NOTES 1 Fir, i alreay LONE? If no, wha i wih i? 2 Wha mahemaical operaion connec an? i ae o i muliplie by i ivie by i i alreay alone i ubrace from 3 Wha i he oppoie of iviing by? 4 Wha mu we alo o if we muliply he righ ie by? iviing by iviing by ino muliplying by muliplying by by ivie he lef ie by muliply he lef ie by ivie he lef ie by ivie he lef ie by Rule 1. To "uno" a mahemaical operaion, you mu o he oppoie. Rule 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. 5 I here more han one mahemaical operaion acing on ""? Ye No Rule 3. If here i more han one operaion going on, you mu uno hem in he oppoie orer in which you woul o hem, he oppoie of he "orer of operaion." pplying Rule 1 an 2 1. To "uno" a mahemaical operaion, you mu o he oppoie. 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. So we uno being ivie by, by muliplying boh ie by. () () The orer of he an oen' maer, bu we uually make hem alphabeical o hey look beer. re we one? 2

3 olving equaion NOTES pplying Rule 4 Rule 4. You can alway wich he lef an righ ie of an equaion. Solving for Le' olve hi equaion for "" = We've now olve our equaion for. harer problem i o olve i for. Tha mean ha when we're one we'll have alone on he lef ie of he equaion. 6 I alreay LONE? If no, wha i wih i? 7 Wha mahemaical operaion connec o? i i alreay alone i being ivie by i being ivie by i being muliplie by i being ubrace from 8 Wha i he oppoie of iviing by? 9 Wha mu we o if we muliply he righ ie by? iviing by iviing by muliplying by muliplying by ivie he lef ie by muliply he lef ie by ivie he lef ie by ivie he lef ie by Rule 1. To "uno" a mahemaical operaion, you mu o he oppoie. Rule 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. 3

4 olving equaion NOTES Solving for T 10 I here more han one mahemaical operaion acing on ""? Ye No 1. To "uno" a mahemaical operaion, you mu o he oppoie. 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. So we uno being ivie by, by muliplying boh ie by. () () Rule 3. If here i more han one operaion going on, you mu uno hem in he oppoie orer in which you woul o hem, he oppoie of he "orer of operaion." re we one? 11 I LONE? If no, wha i wih i? 12 Wha mahemaical operaion connec o? i i alreay alone i being ivie by i being ivie ino i being muliplie by i being ubrace from 13 Wha i he oppoie of muliplying by? iviing by iviing by muliplying by muliplying by by Solving for 1. To "uno" a mahemaical operaion, you mu o he oppoie. 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. = 4

5 olving equaion NOTES 14 I LONE on he lef? i i alone = Solving for v o Le' olve hi equaion for "v o " v = v o + a Tha mean ha when we're one we'll have v o alone on he lef ie of he equaion. 15 I vo alreay LONE? If no, wha i wih i? 16 Wha mahemaical operaion connec a o v o? only a only a i i alreay alone "a" i being ivie by v o "a" i being ae o v o v o i being muliplie by "a" v o i being ivie by "a" v = v o + a v = v o + a 17 Wha i he oppoie of aing a o vo? iviing by v o by "a" ino ubracing v o from "a" ubracing "a" from v o iviing "a" by v o v = v o + a 18 Wha mu we o, if we ubrac "a" from he righ ie? a "a" o he lef ie muliply he lef ie by "a" ubrac "a" from he lef ie ivie he lef ie by v o v = v o + a 5

6 olving equaion NOTES Solving for v o 19 I here more han one mahemaical operaion acing on "v o "? Ye No 1. To "uno" a mahemaical operaion, you mu o he oppoie. 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. v = v o + a v = v o + a a a v a = v o v o = v a Solving for a Le' olve hi equaion for "a" 20 I a alreay LONE? If no, wha i wih i? v = v o + a Tha mean ha when we're one we'll have a alone only v o only v o an i i alreay alone on he lef ie of he equaion. v = v o + a 21 Wha mahemaical operaion connec v o o a? 22 Wha i he oppoie of aing vo o a? "a" i being ivie by v o v o i being ae o "a" v o i being muliplie by "a" v o i being ubrace by "a" iviing by v o by a ino ubracing v o from a ubracing a from v o iviing a by v o v = v o + a v = v o + a 6

7 olving equaion NOTES 23 Wha mahemaical operaion connec o a? 24 Wha i he oppoie of muliplying a by? a i ae o a i muliplie by a i ivie by i ubrace from a v = v o + a iviing a by. iviing by a. muliplying a by muliplying by a v = v o + a 25 Wha mu we o, if we ivie by from he righ ie? ivie he lef ie by a muliply he lef ie by a ivie he lef ie by muliply he lef ie by 26 I here more han one mahemaical operaion acing on "a"? Ye No v = v o + a v = v o + a 27 Which operaion houl we uno fir? 28 Which operaion houl we uno econ? ivie a by ivie a by ubrac v o from a ubrac v o from a v = v o + a v = v o + a 7

8 olving equaion NOTES Solving for a 1. To "uno" a mahemaical operaion, you mu o he oppoie. 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. 3. If here i more han one operaion going on, you mu uno hem in he oppoie orer in which you woul o hem, he oppoie of he "orer of operaion." v = v o + a v o v o v v o = a v v o = a Solving for Le' olve hi equaion for "" v = v o + a Tha mean ha when we're one we'll have alone on he lef ie of he equaion. re we one? Solving for 1. To "uno" a mahemaical operaion, you mu o he oppoie. v = v o + a 2. You can o anyhing you wan (excep ivie by zero) o one ie of an equaion, a long a you o he ame hing o he oher. 3. If here i more han one operaion going on, you mu uno hem in he oppoie orer in which you woul o hem, he oppoie of he "orer of operaion." 8