How do I estimate the instantaneous velocity at a certain time when I am not given the function, but I am given points?

Assuming that this smooth curve represents the motion of the body, estimate the velocity at t=1.0, t=2.5, and t=3.5

(t, s) = (time in seconds, s in feet)
(0, 3.5); (0.5, -4); (1.0, -8.5); (1.5, -10); (2.0, -8.5); (2.5, -4); (3.0, 3.5); (3.5, 14); (4.0, 27.5)

Question

How do I estimate the instantaneous velocity at a certain time when I am not given the function, but I am given points?

Assuming that this smooth curve represents the motion of the body, estimate the velocity at t=1.0, t=2.5, and t=3.5

(t, s) = (time in seconds, s in feet)
(0, 3.5); (0.5, -4); (1.0, -8.5); (1.5, -10); (2.0, -8.5); (2.5, -4); (3.0, 3.5); (3.5, 14); (4.0, 27.5)

anonymous · Answer

This question isn't as difficult as you think it is.
first off, you have to understand what instantaneous velocity is:
Instantaneous velocity is the speed at a one point in time, or instant.

That being said when you are supposed to find the instantaneous velocity at t=1.0 all you need to know is the speed at t=1.0. Lucky for you, this is given to you with the points!

Your speed at 1.0=-8.5
Your speed at 2.5=-5
your speed at 3.5=14

You don't have to do any math here, you just need to understand what the question is asking you for.

Does that make sense? any questions?

anonymous · Answer

-8.5 is the distance (in feet) though lol; not velocity.

anonymous · Answer

I read "s in feet" and assumed it was speed. is this a typo on your end, or is that how the question is written? Or is it s as in displacement...

anonymous · Answer

Yes, s is displacement

anonymous · Answer

usually velocity is measured in meters per second. thats the standard unit

anonymous · Answer

Sorry, my book says feet...

anonymous · Answer

Okay, that makes a little more sense... that's what I get for assuming. Okay, give me a second and I'll see if I can figure is out with displacement.

anonymous · Answer

since 's' is displacement, i think u should divide 's' by 't' to obtain velocity

anonymous · Answer

Yes, mathballet8888 is correct:

think of the equation for distance:
D=V/t
(where D=distance V=Velocity t=time)
now solve for V
V=D/t

anonymous · Answer

yea  velocity=(displacement)/(time elapsed)

anonymous · Answer

Hmm.. that's only the average velocity though. This is a even problem so I don't have the answer in the back of the book, but a very similar problem before this one has an answer in the book... and it has the notation s'(1) (for the 1 sec)... but how do I find the derivative if I do not know the function? o-o