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Do Now

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Objectives K7, K8, K9AP Physics C: Mec han ics

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Age nda

1. Revie w Do Now (5 m in)2. OBJ K7 (30 m in)

3. OBJ K8 (20 m in)4. OBJ K9 (20 m in)

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

Graph ica lly, it is e asy to tell wh e nfun cti on s are zer o. Th e y cross the x-

axis.

Don e with o bjective? No!

Wha t abou t a lgebr a ica lly? Wh e n is afun cti on a t a zer o, max, o r m in?

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

Wh e n is a cert a in k ine ma tic q uan tit yzer o? Set the fun cti on eq ua l to zer o

and f ind ou t .

Wh e n is a cert a in k ine ma tic q uan tit y

at a max o r a m in? Let s look a t agraph and ana lyze

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

Positi on vs Time:

Wha t is s peci a l abou t po in ts C and F ?

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

Max and m in po siti on can be found byloca ting wh ere t he slop e is zer o.

Bu t wha t is t he slop e of po siti on ?

Velocit y! Velocit y is zer o wh e npo siti on is at its max o r m in.

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

Wh ere do you th ink vel ocit y is at itsmax o r m in?

Yes, the ana logy con tinu es . Wh e nacceler ation is zer o, vel ocit y is at its

max o r m in.

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

Bu t wha t abou t acceler ation ? Wha tcom es af ter acceler ation tha t eq ua ls

zer o?

Jerk!

No, no t you. Tha t s wha t a chang e of acceler ation is ca lled. W ell , may beyou too; I don tknow.

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

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K7: Deter m ine wh e n fun cti on s of po siti on, velocit y, o r acceler ation a re zer o, o r ach ieve their max imum o r m in imum va lues .

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K7 Summa ry

To f ind z er oes , set the fun cti on eq ua l to zer o.

To f ind m in and max, set the deriv ative of the fun cti on eq ua l to zer o.Plug in po in ts to d isti ngu ish bet wee n max andm in.

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K8: Cre ate an expressi on fo r a k ine ma tic quan tit ygiven info rma tion in a p roble m and sketc h g raph s of these eq ua tion s.

Wou ldn t it be n ice i f we were tr yingto mod el the mo tion of the p lan ets

and the eq ua tion s of mo tion w erep la in ly writte n in the st ars aroundthe m?

They are n t. We nee d to com e upwith eq ua tion s f rom d escri p tion s of na ture .

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K8: Cre ate an expressi on fo r a k ine ma tic quan tit ygiven info rma tion in a p roble m and sketc h g raph s of these eq ua tion s.

There will be proble ms in phy sics(mo st proble ms) wh ere no eq ua tion s

are give n, just info rma tion.

These are common ly known a s

« Wo rd Pr obl ems ».

Artist re nd eri ng of

wo rd p roble ms

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K8: Cre ate an expressi on fo r a k ine ma tic quan tit ygiven info rma tion in a p roble m and sketc h g raph s of these eq ua tion s.

Yes, there will be eq ua tion s we will beable to « p lug in to » later , bu t tha t

lim its you r br a in sund erst and ing of phy sics .

There fore , we will be gin bycon str ucti ng the eq ua tion s f romscr a tc h.

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K8: Cre ate an expressi on fo r a k ine ma tic quan tit ygiven info rma tion in a p roble m and sketc h g raph s of these eq ua tion s.

Examp le 1:

Find an eq ua tion fo r vel ocit y as a

fun cti on of time if ao = 3 m/ s2 andvo = 2 m/ s.

Sketc h the graph.

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K8: Cre ate an expressi on fo r a k ine ma tic quan tit ygiven info rma tion in a p roble m and sketc h g raph s of these eq ua tion s.

Examp le 2:

Find an eq ua tion fo r po siti on a s a

fun cti on of time if ao = -4 m/ s2,vo = 1 m/ s, and x o = 5 m.

Sketc h the graph.

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K8: Cre ate an expressi on fo r a k ine ma tic quan tit ygiven info rma tion in a p roble m and sketc h g raph s of these eq ua tion s.

Cha llenge Examp le:

Ollie is drink ing wa ter f rom a

wa teri ng ho le . He sees an a lligator and turns away f rom the pond andst arts r unn ing a t 10 m/ s. As he r un saway, h e sl ow s down to a st op a t anacceler ation of -2 m/ s2. How fa r awayf rom the pond is he af ter he com es t oa st op ?

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K8 Summa ry

Use ca lcu lus to f ind n ecess ary eq ua tion s.

Use ca lcu lus to f ind waypo in ts on the graph.Fill in the rest of the sketc h.

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l

mo tion.We ha ve derive d eq ua tion s f rominfo rma tion and there is a pa tter n to

eq ua tion s invo lving a con st an t acceler ation.

Have you no tice d the form of ever ypo siti on eq ua tion ? Velocit y eq ua tion ?

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l

mo tion.

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l

mo tion.

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l

mo tion.Know these 3

eq ua tion s or I will e at you.

Nom. Nom. Nom.

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l mo tion.

Examp le 1:

An ama te ur bow ler rele ases a ba ll

with an in itia l vel ocit y of 2 m/ s; the ba ll slow s down w ith a con st an t ne gative acceler ation of -0.2 m/ s2.How fa r do es the ba ll ro ll be fore st opp ing, and how long do es it take to st op ?

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l mo tion.

Examp le 2:

A runn er bursts ou t of the st arti ng

blocks 0.1 s af ter the gun signa ls the st art of the race . She run s at acon st an t acceler ation fo r the next 1.9 s of the race . If she ha s gon e 8 maf ter 2.0 s, wha t are her acceler ationand vel ocit y a t th is time?

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K9: App ly the eq ua tion s of mo tion invo lvingcon st an t acceler a tion in on e -d ime nsiona l mo tion.

Examp le 3:On a g iven f ligh t , a T-38 tr a in ing jet ha s anacceler ation of 3.6 m/ s2 tha t lasts 5.0 s du ring the

in itia l pha se of take off. Th e af terb urners are the nturne d up to fu ll pow er for an a cceler ation of 5.1m/ s2. The spee d n ee de d fo r take off is 164 kno ts (1 m/ s = 1.94 kno ts ). Ca lcu late the length of runway n ee de d and the to ta l time of take off.

I have a jet .

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K9 Summa ry

Use the kine ma tic eq ua tion s to bypa ss t he ca lcu lus wo rk wh e n you can.