Question

Calculus

Answer 1

it seems like a function of sin or cos

Answer 2

detail explanation please, I don't get this problem at all:"(

Answer 3

really??

Answer 4

what do you know of sntiderivatives, or integration?

Answer 5

x"(t)=7cost

Answer 6

can u integrate it ??

Answer 7

You're given \(a(t) = 7\cos(t)\) with the conditions that it starts at rest (i.e. \(v(0)=0\)) and that it's initial position is 9 (i.e. \(f(0)=9\)).

To find velocity, integrate \(a(t)\) to get \(\displaystyle v(t) = \int 7\cos t\,dt = 7\sin t+C\). Apply the condition \(v(0) = 0\) to get \(C=0\) (verify).

Hence \(\boxed{v(t) = 7\sin t\). Do the same thing for finding \(f(t)=\displaystyle\int v(t)\,dt\) and apply the initial condition to find the integration constant.

Answer 8

i can derive them easily now, integrate some i get wrong

Answer 9

\(\boxed{7\sin t}\) *

Answer 10

\[v(t)=\int\limits x"(t)dt\]

Answer 11

after it again integrate v(t)

Answer 12

\[x(t)=\int\limits v(t) *dt\]

Answer 13

since you're given intial conditions, you may use definite integral also :

\[\large v(t) - v(0) = \int\limits_{0}^ta(t) ~dt\]

Answer 14

so then on the top part you initially only use the second derivative?

Answer 15

sorry I am still analyzing the steps

Answer 16

okay hold on i kinda get it...

Answer 17

\(\large v = \int a\)

you need to know that upfront to work this problem

Answer 18

Oh it was already mentioned in the start of question

Answer 19

yes in the first sentence, but I don't get how after you hence & do the same thing? You get what im asking?

Answer 20

How Cristopher explained it, I get it and know how to do it, but I dont' know what my answer will be, like when to stop

Answer 21

There is usually videos of an example i see before solving the problem, but this one doesn't have any examples

Answer 22

Christopher already gave you an expression for velocity function.
\[\large v(t) = 7\sin t + C\]

You just need to plugin the initial condition to find the value of constant C

Answer 23

the initial condition comes from the fact the body is at rest to start with

Answer 24

v(0) = 0 is your initial condition

Answer 25

okay give me a second, oh thats why it explains it with particle!! and its zero then

Answer 26

yes 0

Answer 27

i get why on that part now

Answer 28

good, so whats your final velocity function ?

Answer 29

v(0)=7sin(0)+C

Answer 30

thats the equation for solving C

Answer 31

v(0)=7sin(0)+C = 0

Answer 32

solve C and plug it in velocity function

Answer 33

& its position is x = 9.? I don't need that yet?

Answer 34

7sin(0)+C = 0

7*0 + C = 0

C = 0

so the velocity function would be :
\[v(t) = 7\sin( t) \]

Answer 35

v'(t)=7t

Answer 36

thats what i got, for the final not v(t) 7 sin t

Answer 37

v'(t) represents acceleration and you're given a = 7cos(t)

so what do u mean by v'(t) = 7t ?

Answer 38

and what happened to sin's and cos's :O

Answer 39

ahhhh idk what i did.... i thought we wouldn't include them for the final, answer

Answer 40

:(

Answer 41

hmm

Answer 42

so it is at rest at -7?

Answer 43

right?

Answer 44

I'm going to submit it now, because its due already, but i would like to keep working on the problem to practice it, I won't know if i get it right though because webassign closes

Answer 45

is that fine? Because I'm sure it will be on my next exam

Answer 46

wait

Answer 47

whats ur answer for v(t) and f(t) in part a ?

Answer 48

i don't have anything for f(t) i have a 90% so far so i should be good

Answer 49

-7 is for part C

Answer 50

i know for f(t) we factor at the end from V(t)

Answer 51

I see why you're rushing :)
christopher already gave u an answer for v(t) :
\[v(t) = 7\sin (t)\]

Answer 52

yes i have that :)

Answer 53

you haven't noticed it because you're just rushing

Answer 54

i just have one blank so i should be good

Answer 55

simply integrate that to get f(t)

Answer 56

I saw the answer from christopher, but didn;t get it

Answer 57

okay i submitted it, my answer for v(t) was right, my other one was - 7cos(T)+C

Answer 58

but it was wrong so i think i did something wrong, i overall got an 94%, but what was f(t) then?

Answer 59

thats a good try, you need to find the value of C and plug it in back for f(t) also

Answer 60

oh shoot thats true! like the previous one

Answer 61

yes but you don't want 100%, so..

Answer 62

yes i do lol

Answer 63

you're so happy just by getting 90 that you want to submit the homework without even giving a good try for the last q

Answer 64

I just studied for my ochem exam and forgot my calc hoemwork:/

Answer 65

I didn't submit it, it submits at 12:59 lol

Answer 66

Ohkiee

Answer 67

plus i'm doing fairly good on exams:)

Answer 68

are these really exams or homework ?

Answer 69

homework, but those are my past exams

Answer 70

you should aim for 100 in calc

Answer 71

look let me show you

Answer 72

The date of my exam was Oct 31st lol , not Nov 5th, we can't post any exams on open study!!! @ganeshie8 :)

Answer 73

Yea, we should aim for 100's in all the classes!

Answer 74

@ganeshie8 Thank you for all your help!
I need to look at more videos