Question

a particle moves along the x-axis so that its velocity at t >/= 0 is given by v(t)=1-sin(2pi(t))

- find acceleration a(t) of the particle at any time t

Answer 1

the derivative of velocity is acceleration

Answer 2

you got a teacher telling you to post this here by chance? this is coming up alot

Answer 3

yeh,, it's for school

Answer 4

how do i find the derivative?

Answer 5

the derivative is explained in your material :)

\[\frac{d}{dt}(1-sin(2\pi\ t))= \frac{d}{dt}1-\frac{d}{dt}sin(2\pi\ t)\]

Answer 6

the derivative of a constant is?

Answer 7

so it would be -cos 2 pi?

Answer 8

yes, except for one minor detail; the "t" parts

Answer 9

sin(nt) pops out the derivative of nt

Answer 10

chain rule

Answer 11

sorry i dont understand

Answer 12

how do you find the derivative of t/

Answer 13

\[-\frac{d}{dt}sin(2\pi\ t)=-cos(2\pi\ t)*\frac{d}{dt}2\pi\ t\]

Answer 14

1-cos2pi sin t?

Answer 15

o ok! got it

Answer 16

good luck ;)

Answer 17

so final answer is 1-cos2pi x 2pi(t)

Answer 18

2pi t is just a constant * t; kt

the derivative of say: kt is k

sooooo, 2pi t derives to 2pi

Answer 19

so 1-cos2pi x 2pi

Answer 20

and the "1" part derived to zero so its not included in the end

\[\frac{d}{dt}(1-sin(2\pi\ t))=-2\pi\ cos(2\pi\ t) \]

Answer 21

o ok

Answer 22

the follow up question is find all values of t 0</= t </= 2 for which the particle is at rest

Answer 23

do i set the original equation = 0

Answer 24

when the derivative = 0; we are at rest; the derivative of position is velocity; and 0 velocity is resting

Answer 25

in this case; when cos(2pi t) = 0 we are at rest

Answer 26

so we set the original to 0 to find at rest/

Answer 27

2pi t = pi/2
t = 1/4

2pi t = 3pi/2
t = 3/4

Answer 28

no, the original is postiion. set the derivative to zero to determine when there is no velocity; when its standing still; when its not moving; when it is at rest

Answer 29

position tells us WHERE we are

derivative of position = velocity; tells us HOW FAST we are moving

Answer 30

but isnt our derivative 2pi cost (2pi (t)

Answer 31

yes; and when is that equal to 0?

Answer 32

cos = 0 at pi/2 (90) and 3pi/2 (270)

Answer 33

so when 2pit = pi/2 OR 2pit = 3pi/2

we are at 0 velocity

Answer 34

might wanna check to make sure we hit all the 2 values between 0 and 2 tho; theres prolly a few more to hit

Answer 35

all the "t" values between .... that is

Answer 36

2pi t = (2n+1)pi/2

2 t = (2n+1)/2

t = (2n+1)/4

0 < (2n+1)/4 < 2

0 < 2n+1 < 8

-1 < 2n < 7

-1/2 < n < 7/2

Answer 37

its 0 to 2 thanks