Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin πt + 5 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)

Answer 1

looks like Simple Harmonic Motion
- but whats your question?

Answer 2

i dont know displacement formula and everyone says derive it but we havent learned that yet...

Answer 3

it says two people replied to this but i can only see the one. and it doesnt say im the other..

Answer 4

What's the actual question here?

Answer 5

im supposed to find the average velocity

at

1.01
1.001
and instant

Answer 6

And in the question is it
3 sin(πt) + 5cos(πt)
or
3 sin(π)t + 5cos(π)t
or ?

Answer 7

well the question doesnt have parentheses in it but ive been doing it (pi)t

Answer 8

i mean (pit)

Answer 9

see ive been plugging in and i get like crazy numbers

Answer 10

Since you haven't learned derivatives yet, you can use this site to find them:

http://www.wolframalpha.com

For this problem, I used this (because I'm lazy):
http://www.wolframalpha.com/input/?i=derivative+of+3sin%28pit%29+%2B+5cos%28pit%29

Answer 11

then i subtract the derivative with the other time and divide by difference of time?

Answer 12

Here's the right equation (I cut and pasted the original one before :)
\[\pi(3cos(\pi t) - 5sin(\pi t))\]Just plug in t for the different times you need to get the velocity.

Answer 13

I would just take the first and last velocities and divide them by two to get the average velocity over the period in question.

Answer 14

like 1.001 and 1 and then 1 and 2?

Answer 15

Not sure what you mean but the formula for average velocity would be:\[V_{avg}=\frac{V_{initial}+V_{final}}{2}\]

Answer 16

However, after rereading your response above, my guess is that they just want the velocity at these particular times:

1.01, 1.001 and instant (0)

Answer 17

right

Answer 18

so do i use that formula still?

Answer 19

So you're going to end up with 3 values...one for each time.

Yes...so for the first one you do this:
\[\pi (3cos(π*1.01)−5sin(\pi * 1.01))\]

Answer 20

and then dont i subtract \[\Pi(3\cos(\Pi \times1)-5\sin (\Pi \times1) \]

Answer 21

then divide by .01?

Answer 22

I lost you... You have the equation for velocity which is the rate of change in displacement...we got that by taking the derivative of the displacement equation.

All you have to do at this point is take your 3 values of t (1.01, 1.001, and 0) and plug them into the equation to get the value of the velocity at each point in time.

I'm not sure why you want to subtract or divide or do anything else :)

Answer 23

hahaha because i like making it more complicated? :P haha

Answer 24

a bit :)

Answer 25

Here
For a value of t=1.01 you should get 8.541 m/s
For a value of t=1.001 you should get 8.549 m/s
For a value of t=0 you should get 9.425 m/s

Answer 26

it didnt work :[

Answer 27

Can you elaborate?