Linear Kinematics : Velocity

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Linear Kinematics Velocity Acceleration
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Speed
Displacement - the change in position in a
particular direction and is always a straight
line segment from one point to another. Displacem
ents are vector quantities and can be combined in
vector fashion. Motion the displacement of an
object in relation to objects that are considered
to be stationary. The rate of motion is called
speed
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e.g. you are riding a bike at 6 m/s You travel 6
m in 1 second, 12 m in 2 seconds.
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Speed can be graphed with a displacement vs. time
graph.
Slope A 3/1 3 m/s Slope B 3/3 1 m/s Slope
C 1/3 0.33 m/s
This graph shows three lines of constant speed.
In other words, the speed remained the same over
the entire displacement and the result is a
straight line graph.
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A graph of your speed might look like fig 3-3
The average speed is found by dividing the total
distance by the elapsed time. In most cases
objects do not move with a constant speed.
Initially and at the end, the speed is likely to
be less. Suppose you ride your bike 120m in 20s.
Your average speed is 6m/s
You start at 0.0 m/s, increase to a constant
speed between 3 and 15 s then begin to slow down.
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Instantaneous speed is the slope of the line at a
point in the line. This would be shown by the
slope of the line that is tangent to the speed
curve. Without calculus, the only way to measure
instantaneous speed is to calculate the slope of
a tiny portion of the speed curve.
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On our graph, the initial speed A is approx. 3.9
m/s, the constant speed B is approx. 7.5 m/s, and
the final speed C is approx. 4.5 m/s.
Speed is a scalar quantity, meaning that no
direction is implied. It is
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Velocity
Velocity is speed in a particular direction.
When you are given the speed of the object and
the direction it is headed, you know the
velocity. This makes it a vector quantity.
Remember velocity may be positive (ve) or
negative (-ve) to indicate some direction.
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Recall that ? is the Greek symbol delta and means
change in
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In this graph, (fig 3-4) the velocity over the
entire range is constant
Similarly, the velocity between points A and B on
the graph is
The motion of this object is said to be uniform
(i.e. it doesn't change through the graph).
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A graph with variable motion is shown in fig 3-5.
The average velocity is
The velocity between points C D is
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The velocity at the specific point C is found by
drawing the tangent and finding its slope.
The velocity at a specific instant in variable
motion is also called instantaneous velocity.