# Instantaneous velocity and average velocity

hi all having a problem with this question:

The position of a rabbit along a straight tunnel as a function of time is plotted: http://img284.imageshack.us/img284/5764/untitled0vz.png [Broken]
1. What is its instantaneous velocity at t = 10.0s and t=30.0s
2. what is the average velocity:
between t = 0 and t = 5.0s
between t = 25.0s and t = 30.0s
between t = 40.0s and t = 50.0s

i can do it when they give an equation. and i know it has to all do with tangents and all that, i can get the results by "estimating", but not as accurate. im totally stuck with this one any help at all will be appreciated.

thanks

Last edited by a moderator:

Chronos
Gold Member
Last edited by a moderator:
Instantaneous means the derivative at that point in time; average is the slope formed between the points.

Knavish said:
Instantaneous means the derivative at that point in time; average is the slope formed between the points.

yeh i know that but how do you get the equation? i understand taking 2 points eg. (x1,y1)(x2,y2) but i cant find a reliable way of finding them

Struggling said:
yeh i know that but how do you get the equation? i understand taking 2 points eg. (x1,y1)(x2,y2) but i cant find a reliable way of finding them
this problem is to determine instant velocity GRAPHICALLY.
you don't need any "equations" in the usual sense.
instant velocity is the SLOPE of the tangent line at a point along the curve.
just determine the slope of the tangent line using (Δx/Δt) by choosing 2 points along the tangent line (1 point can be that at which the tangent line is tangent to the curve) and calculate (Δx/Δt)=(x2 - x1)/(t2 - t1). see this diagram:
http://www.andamooka.org/newtphys/figs/bk1/ch02/motiond.JPG [Broken]

Last edited by a moderator:
HallsofIvy