Unit 5: Motion and Forces
Average Velocity and average Speed
A very compact way to represent or describe position is with a graph of position x plotted as a funtion of time t [a graph of x(t)]. The red line on graph on the left shows the position of a statiponary student 2m from me. The student's position stays at 2m.
The yellow line describes another student who was stationary for a while but began to move towards me and then away from me with some kind of regularity.
The solid green line describes a more random kind of motion.
One of the bits of information we can extract from the graph is how fast the people were moving. This quantity is called the average velocity (v_{avg}).
v_{avg} = [^{Δx}/_{Δt}]
v_{avg} = [(x_{2}  x_{1})/(t_{2}  t_{1})_{}]
The Unit for this quantity is ms^{1 }(m per second) sometimes written m/s. In terms of dimensions it is LT^{1} (length / time).
In graphical terms v_{avg} is the slope of the straight line which connects the two particular points (x_{2},t_{2}) to (x_{1},t_{1}) on the x(t) line (often alled curve).
Like displacement described earlier, v_{avg} has both magnitude and direction. If v_{avg }is positive
then the line slants upwards and when negative the line slopes downwards.
Note v_{avg} always maintains the sign of Δx as t is always positive.
Example:
Calculate the average velocity in the between (a) x_{2} and x_{1} (green line) (b) x_{2}  x_{1 }(yellow line):
(a) v_{avg} = [^{Δx}/_{Δt}]
v_{avg} = {[0  (5)]/[2  (3)]
v_{avg} = [(5)]/(5)]
v_{avg} = 1.0 ms^{1}
v_{avg} = [^{Δx}/_{Δt}]
v_{avg} = {[4  (5)]/[3  (2.5))]}
v_{avg} = [(9)/(5.5)]
v_{avg} = 1.64 ms^{1}
Average speed s_{avg} is a different way of describing “how fast” a particle moves. While average velocity involves the particle’s displacement Δx, the average speed involves the total distance covered and is independent of direction.
v_{avg} = [^{Distance covered}/_{time taken}]
Note: Aaverage speed does not include direction and so lacks an algebraic sign.
Question.
You drive along a straight road heading North for 10 minutes at 20 ms^{1}. What is your displacemnt?
