Question

A particle moves along a line so that its position at any time t is greater than or equal to 0 is given by the function s(t) = t^2-3t+2. Where is the particle when s is a minimum?

Answer 1

you know how to find the minimum value of a quadratic ?

Answer 2

I don't remember. My teacher wanted us to use derivatives and such I think

Answer 3

yes, if this question belongs to calculus, derivatives,
\then find the derivative of s(t)

Answer 4

Well I'm in calculus, I just don't know how to solve the problem

Answer 5

The derivative of s(t) is 2t-3

Answer 6

My original idea was to set v(t) equal to 0, but that gives me the place where is changes directions

Answer 7

thats correct
to get the minimum
just set
s'(t) = 0
get t

Answer 8

Wait, but doesn't that give me the place where the particle changes directions?

Answer 9

where did you read that ?

s'(t) = 0 gives you extreme points,
max. or min value of s

Answer 10

Velocity changes directions when it hits 0

Answer 11

My book and teacher said that

Answer 12

A particle is moving forward when velocity is positive, and it is moving backwards when it is negative. It is changing directions when it hits 0.

Answer 13

ok, might be true,
but it gives maximum or minimum for the displacement function too

Answer 14

Ok, now I'm really confused

Answer 15

Wait, so they are the same, so that means that it hits 0 at 3/2

Answer 16

So it stands still AND has a horizontal tangent line at 3/2

Answer 17

at t=3/2 the particles displacement is minimum!

Answer 18

not sure what u mean by "stand still"

Answer 19

if you mean 0 displacement, then its not true

Answer 20

Its not letting me hit the post button because i typed too much and the chat it blocking it xD

Answer 21

So when the position function (s(t)) hits a minimum, it will head back up towards 0, so it is changing directions. When s(t) is at a minimum, its derivative, the velocity function, hits 0,

Answer 22

So to find where the particle changes directions, you have to find where the velocity function hits 0, because this tells you that the position function is at a minimum and will head up towards 0.

Answer 23

Does that make sense at all?

Answer 24

"So when the position function (s(t)) hits a minimum, it will head back up towards 0,"

i don't understand this

it will be back to 0 when s(t) = 0
it would be minimum when s'(t) = 0

Answer 25

because by minimum, it can be negative too

Answer 26

No, what I mean is that when the position function hits a minimum, the particle is going to change directions and move back towards its original position

Answer 27

And if the particle is moving on a number line, its original position was 0. All I mean is to show that the particle was changing directions

Answer 28

Is that any better?

Answer 29

So to find where it changes directions, you have to set v(t)=0 and to find where the particle is when s is a minimum, you have to plug the value that it changes directions into s(t)

Answer 30

THE POSITION GRAPH IS CHANGING DIRECTIONS WHEN V(T)=0. Thats what Im asking

Answer 31

lol

Answer 32

yes, better explained now
and agreed,
and that will give you the position

in this case if you plug in t=3/2
it gives you minimum value of the position

Answer 33

Ok, that makes so much more sense now. Thanks for bearing with me!!!

Answer 34

thanks for giving that explanation, just got a new insight to this whole thing! :D