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Level 6

Vectors - Addition, Subtraction, Components, Scali


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direction and magnitude (size)
The velocity vector has both _
Scalar Quantity
a measure of magnitude
its initial position to its final position at some later time
the displacement of an object is a vector that is drawn from_
what is the displacement vector of an object?
the displacement vector is a straight-line connection from the object's initial to his final position, not necessarily his actual path
Magnitude...
... of a vector is always a positive quantity
net displacement is the vector
from the initial position to final position
resultant vector
the sum of two vectors is called_
what are the rules of multiplication of vectors by scalar numbers?
Multiplying a vector by a positive scalar gives another vectors of different magnitude but pointing in the same direction
zero vector
a vector of length zero.
How can we perform subtraction between vectors?
With numbers, subtraction is the same as addition of a negative number
Cartesian coordinate system
which type of coordinate system will you use for physics problems?
component vectors
vectors that are parallel to the axis of the Cartesian coordinate system
x-component vector
the vector (projection) along the x-axis
y-component vector
the vector (projection) along the y-axis
what means to "descompose or resolve" a vector?
broke a vector into two perpendicular vectors that are parallel to the coordinate axes (component vectors)
component
A part or element of a larger whole.
vector
a displacement distinguished by magnitude and direction but not by location.
displacement
A change in position (delta p).
Scalars
have only a magnitude e.g. speed, distance
length
A measured distance
vector addition
-mathematical operation combining 2 vectors A and B to form a third resultant vector R, the "vector sum" of A and B
If A and B vectors are in the same direction, their vector sum _
has magnitude equal to the sum of of the magnitudes of A and B
magnitude equal to the difference in the magnitudes of A and B
If vectors A and B point in opposite directions, their vector sum has_
the negative of a vector A, is defined to be _
the vector of the same length as A, pointing in opposite direction
the addition of a negative vector
vector subtraction can be seen as the_
A vector may be described quantitatively in 2 different ways:
by describing its magnitude (size) and direction or describing its horizontal and vertical components
meters
the units of the magnitude of a vector could be _(3 examples)depending on which particular _
The direction of a diagonal vector is indicated by an_. Also by _
angle measured relative to coordinate axes placed at the tail of the vector
counterclockwise from the +x-axis (clockwise if the angle is negative)
If the angle is stated without a qualifier, the angle is assumed to be measured _
no
Does zero acceleration mean zero velocity
by using its horizontal and vertical components
What is the second method to describe a vector?
vector components
the lengths of a vector along specified directions
Vx can only Point to left or right
Vx can only point in which directions? Vy Can only point in which direction? Explain why we use positive and negative signs with the component vectors
Scalar components (other name)
or simply components of vector v
the standard coordinate axes are assumed
How we assign the positive and negative to the component vectors?
vector: a (with an arrow above the letter)
Name the notation used with the Vector A (vector, vector components, components, magnitude)
-Position: r (with arrow above the letter)
Name the notation used with position (vector name, vector components, components, magnitude)
-Displacement: (triangle) r (arrow above r)
Name the notation used with the displacement (vector name, vector components, components, magnitude)
sine
opposite/ hypotenuse
cosine
adjacent/ hypotenuse
solve sine for opposite
opposite= h sin (delta)
solve cosine for adjacent
adjacent= h cos (delta)
tangent
opposite/adjacent
delta= tan?¹ (opposite/adjacent)
solve equation for delta
h= (square root of) (opposite² + adjacent²)
write expression of hypotenuse in terms of a and o
A vector quantity is one described by both a_
magnitude (size) and a direction (often an angle relative to one of the coordinate axes)
velocity
what are 3 examples of vector quantities?
a magnitude only
scalar quantities are ones described by_
Speed
Units: cm/s, m/s, mi/hr, km/s ...
arrows
In graphical form, vector quantities are represented by_
the pointed end of the arrow
what is the "head" of an arrow?
What is the "tail" of an arrow?
the opposite end to the arrow in a vector
The Length of the Arrow
The magnitude of a vector in a scaled vector diagram is depicted by _______ __ _______
What represents the direction of a vector?
the arrow points in the direction of the vector quantity
How vectors are symbolized?
by a letter with a small arrow above it (small arrow does not point in the direction of the vector; it merely symbolize that the vector by a quantity has a direction associated with it)
what is the position of an object represented by a vector?
the position of an object is a vector whose tail is located at the origin and whose head is located at the location of the object
r (with an arrow above it)
what symbol is used to represent a position vector?
What is the magnitude of the position vector?
is a distance measured in meters in the SI system of units
what is the origin in the position vector?
the origin is an arbitrary point in space that has been chosen to represent zero
define displacement of an object during an interval of time (include other name for this)
displacement of an object during an interval of time (also called change in position of the object) is defined as the difference between the position of the object at the end of the time inte…
How displacement is symbolized?
(triangle, which means change) r (arrow above)
rf=ri + (traingle)r
How determine the final position of an object?
draw arrowheads on each vector
To draw a diagram that correctly illustrates the sum of the two vectors you must both_
of the same magnitude but the opposite direction
the negative of a vector is a vector_ (include how to symbolized)
the subtraction a vector can be through_
the addition of the opposite of the vector
head to tail
To add two vectors the need to be arranged_
the average velocity of an object is defined as_(include formula)
the ratio of the displacement of the object and the corresponding time interval
m/s²
what are the SI units of the average velocity?
How the average velocity is obtained by using vector?
is obtained by dividing a vector (displacement) by a scalar (the time interval)
the definition of average acceleration is the_ (include formula)
ratio of the change in velocity over the time interval
two instantaneous velocities
The definition of acceleration involves the difference between_
instantaneous velocity is defined as the _
limit of the average velocity as the time interval approaches zero
How the direction of the instantaneous velocity compared with the direction of the displacement vector?
the direction of the instantaneous velocity is the same as the direction of the ratio in the limit which is the same as the direction of the displacement vector in the numerator of the ratio