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Summary Notes for STEM12
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Lecture notes for Grade 12 STEM
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The instantaneous speed of a body is its speed at a particular time, with △t being extremely small.The speed indicated by speedometer is instantaneous speed. Velocity is the displacement of a body
per unit of time. Thus, it is a vector quantity. Average velocity is the total displacement per unit in time.
In symbol, v= d/t
Acceleration refers to the change in velocity with respect to time. Since acceleration is defined in
terms of velocity, which is a vector quantity, then acceleration is also a vector quantity. Velocity can
change in three ways: (a) change in speed, which maybe either an increase or decrease; (b) change in
direction; and (c)change in both speed and direction. Thus, a body is said to be accelerating when it is
moving with changing speed, with constant speed but with changing direction. In symbol, a =
(△v)/(△t) = (v-v0)/t
⮚ Scalar is a quantity with magnitude and usually a unit of measure.
⮚ A vector is a quantity with magnitude, direction, and usually a unit of measure.
⮚ Displacement is a vector quantity indicating (1) the distance from one point to another and (2) the
direction of an arrow pointing from the first to the second point.
⮚ Distance is the corresponding scalar quantity; it indicates only the separation of the points, not the
direction from one to the other.
VECTORS AND DIRECTION
Examples of vector quantities that have been previously discussed include displacement, velocity,
acceleration, and force. Each of these quantities are unique that a full description of the quantity
demands that both a magnitude and a direction are listed. For example, suppose your teacher tells you
"A bag of gold is located outside the classroom. To find it, displace yourself 20 meters." This statement
may provide yourself enough information to pique your interest; yet, there is not enough information
included in the statement to find the bag of gold. The displacement required to find the bag of gold has
not been fully described. On the other hand, suppose your teacher tells you "A bag of gold is located
outside the classroom. To find it, displace yourself from the center of the classroom door 20 meters in a
direction 30 degrees to the west of north." This statement now provides a complete description of the
displacement vector - it lists both magnitude (20 meters) and direction (30 degrees to the west of north)
relative to a reference or starting position (the center of the classroom door). Vector quantities are not
fully described unless both magnitude and direction are listed.
Representing Vectors
Vector quantities are often represented by scaled vector diagrams. Vector diagrams depict a vector by
use of an arrow drawn to scale in a specific direction. Vector diagrams were introduced and used in
earlier units to depict the forces acting upon an object. Such diagrams are commonly called as free-body
diagrams. An example of a scaled vector diagram is shown in the diagram at the right. The vector
diagram depicts a displacement vector. Observe that there are several characteristics of this diagram
that make it an appropriately drawn vector diagram.
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