Question

The displacement (in meters) of a particle moving in a straight line is given by s=t^2-5t+16. Find the average velocity of the time interval (3,4) please help. no idea

Answer 1

Let the time interval be (x,y).
Then the average velocity during that time interval will be
v=(s_y-s_x)/(y-x)
v=(s_4-s_3)/(4-3)
s_4=4^2-5(4)+16
s_3=3^2-5(3)+16

Answer 2

Am i right @hartnn?

Answer 3

i didn't know about this method, i would have used calculus...(integration)...don't know whether the asker can/should use calculus.

Answer 4

hmm k. i too got to know this method recently only.

Answer 5

Yes it is for calc

Answer 6

I need to solve it in terms of calculus but I don't know how to get the answer

Answer 7

do u know the relation between displacement and velocity?

Answer 8

well just the formula f(a+h)-f(a)/h that's all I have

Answer 9

no not at all, but this a question for my homework that is due tonight

Answer 10

R u there?

Answer 11

yup.
that formula is similar to one used by ajprincess in first comment, could you understand that?

Answer 12

not exactly. I understand in terms of (x,y) but have no idea what she is doing with it. Perhaps you can explain what to do please if its not to much?

Answer 13

sure.
u have V= s(t+h)-s(t)/h
where V is the average velocity and s(t) =s=t^2-5t+16.
now you have interval (3,4) , so we put t=3, h=1
we get
V= (s(4)-s(3))/(1)
Did u get this much ??

Answer 14

ask if there is any doubt in any step

Answer 15

yes I got that far I am just checking my algebra. Why did you put h=1?

Answer 16

h= time interval = 4-3 = 1

Answer 17

or you can say change in time = 4-3=1

Answer 18

ok thank you. I got it. So for the answer did you get 2 or am I totally wrong?

Answer 19

what did u get s(4) and s(3) as ?

Answer 20

oh, yes even i am getting +
its correct :)

Answer 21

+2

Answer 22

yes 2 right? So basically I am plugging those numbers instead of t right?

Answer 23

yes, s(4) means put t= 4 in s(t)

Answer 24

and remember you are also dividing by time interval

Answer 25

yes but h will still be 1 right?

Answer 26

since 4-3=1

Answer 27

in this problem, yes, h= 1

Answer 28

any more queries ?

Answer 29

I got it Thank you so much for your help. I really appreciate it

Answer 30

welcome ^_^ and
\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

Answer 31

Thank you!

Answer 32

Sorry cud nt explain u my answer. had to go in the middle:(. Thanx @hartnn for explaining it. great work @hartnn:)