Question

can someone please explain this step by step to me?

Answer 1

@amistre64

Answer 2

@ikram002p

Answer 3

s(t) = 5cos(t) − sin(3t)
first derivative gives the velocity , right ?
second derivative gives the acceleration , could u try it please ?

Answer 4

find out derivative?

Answer 5

is it 0

Answer 6

how ?

Answer 7

i dont really know second derivatives, this is a practice test for the module and i like learning about it before i actually do it and im completely confused. could you write the steps out fo me

Answer 8

first derivative is s'(t)
can u find it ?

Answer 9

-5sin(t)-3cos(3t)

Answer 10

@ikram002p

Answer 11

can you plz write steps

Answer 12

yes , now second derivative is the first derivative of -5sin(t)-3cos(3t) :)

Answer 13

now take derivative for
-5sin(t)-3cos(3t)

Answer 14

9sin(3t)-5cos(t)

Answer 15

yes :)
so the velocity would be the first derivative of the position function
v(t)=s'(t)=-5sin(t)-3cos(3t)
while the acceleration is given by the second derivative of the position function or the first derivative of the velocity function like this
a(t)=v'(t)=s''(t)=9sin(3t)-5cos(t)

Answer 16

back to ur question ,
` What is the acceleration of the particle at time t = π seconds?`
you found acceleration , which is
a(t)=9sin(3t)-5cos(t)
now all u need is to find a(π ) :) , good so far ?

Answer 17

yess

Answer 18

let me know if u have doubt , and if u saw some weird symbols just refresh the page :)

Answer 19

sorrry openstudy signed me out @ikram002p what do i do next?

Answer 20

a(t)=9sin(3t)-5cos(t)
now all u need is to find a(π ) :)

Answer 21

so replace 2 with pi? i dont get it ..

Answer 22

t*

Answer 23

like i dont get what you mean..

Answer 24

yes replace :O
which part u dont understand ?

Answer 25

so its going to be 9sin(3pi)-5cos(pi)

Answer 26

im getting a weird answer

Answer 27

Yes, you plug in pi in the second derivative, what did you get?

Answer 28

-3.51

Answer 29

which makes no sense

Answer 30

Mhm, not sure how you did that, what is sin(3pi) ?

Answer 31

Go back to trigonometry, and the special triangles :)

Answer 32

You should get a whole number

Answer 33

0?

Answer 34

Right!

Answer 35

what is cos(pi)?

Answer 36

-1

Answer 37

Right right! So -5*-1? :)

Answer 38

5 (:

Answer 39

There you go!

Answer 40

thank you !!

Answer 41

In calculus, the starting process is the calculus part mostly, and then towards the end it slowly goes back to high school math ;). Just a little secret.