1. Velocity (s-t) Graphs
Example 1:
This general graph represents the motion of a body travelling at constant velocity. The graph is linear (that is, a straight line).
Recall that linear equations have the general form
y = mx (m is a constant and x is a variable).
The number m is called the slope of the line (
).
In the above graph, we have the function:
displacement = velocity × time
or
s = v × t
Velocity is constant and time is a variable.
We note that the graph passes through (0,0) and has slope
v. The slope of the line tells us the velocity. We can
also write the velocity using delta notation:
which means "change in displacement
over change in time".
If we have a high velocity, the graph has a steep slope. If we have a low velocity the graph has a shallow slope (assuming the vertical and horizontal scale of each graph is the same).
High speed Low speed
Example 2
A marathon runner runs at a constant 12 km/h.
a. Express her displacement travelled as a function of time.
b. Graph the motion for 0 ≤ t ≤ 4 h
Displacement-time Graphs
Example 1
This is the graph of a journey by sports car:
a. What is the velocity for each stage of the journey?
b. What is the average (mean) velocity for the whole journey?
Example 2
A particle in a magnetic field moves as follows:
Find the velocity for each part of the motion.
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