# Velocity: Speed and Direction/ Motion diagrams/ instantaneous velocity/ Uniform Motion

-constant speed
-Particle that moves equal distances in equal time intervals
-objects that are neither speeding up nor slowing down
-for an object in uniform motion, successive frames of the motion diagram are equally spaced (object’s displacement is the same between successive frames)
Uniform motion (include 3 definitions and how it would be represented in a motion diagram)
the greater the distance traveled by an object in a given interval, the greater the speed
how would you know the speed of an object in a motion diagram?
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speed= distance traveled in a given interval / time interval
what is the speed formula?
-that it does not show any direction in the motion
-velocity
what is the problem of speed? what is used instead?
velocity= displacement / time interval
write the velocity formula
-bicycles are traveling opposite directions
-because one bicycle can go in positive direction, while the other bicycle goes in negative direction (taking into account origin) since velocity shows direction but speed does not
how two bicycles can have the same speed but different velocity?
-how fast an object moves
-both an object’s speed and its direction
speed measures only_, but velocity tells us _
-movement to the right
-movement upward
a positive velocity indicates which two motions in one dimension?
-movement to the left
-movement downward
a negative velocity indicates which motions in one dimension?
-speed is always positive
-velocity can be either negative or positive
which is always positive: speed or velocity? which can be either negative or positive?
average velocity
the velocity of the entire motion is called_
the velocity of an object at a particular instant in time
instantaneous velocity
distance (feet, meter, miles) over unit of time (seconds, hours)
what are the units of speed and velocity?
an object travels X distance for each x time unit of elapsed time
ex: 23 m/s=23 meters for each 1 second elapsed time
what does exactly “per” means?
-when a physical quantity is described by a single number (with a unit)
-ex: time, weight, temperature
-it can be positive, negative, or zero
scalar quantity (definition, 3 examples, and what 3 things it can be)
is a quantity that has both size (how far? or how fast?) and direction (which way?)
Vector quantity
-the size or length of a vector
-it can be positive or zero, but it cannot be negative
magnitude (definition and what can be? (3))
arrow, as illustrated for the velocity and force factors
we graphically represent a vector as an_, as illustrated fro the_and_factors
The arrow is drawn to point in the direction of the vector quantity, and the length of the arrow is proportional to the magnitude of the vector quantity
How you would draw a vector correctly?
we do this by drawing an arrow over the letter that represents the quantity
ex:

A
how do we represent a symbol to be for a vector instead for a scalar?
-displacement vector

ds
since the displacement has both direction and magnitude (how far?), it can be represented as a vector, which is called_, which its symbol is_
-initial position
-its final position
-the actual path followed between these two points
An object’s displacement vector is drawn from_to_, regardless of_
-vector drawn between the initial starting position to the final overall position while using two or more displacements
-sum of two or more displacements that made it up
net displacement vector
→ → →
dnet= d1 + d2
How can we represent a net displacement vector while having two displacements (d1 and d2)?
-vector addition obeys different rules from the addition of two scalar quantities
-The direction of two vectors, as well as their magnitudes, must be taken into account
-we can add vectors together by putting “tail” of one vector at the tip of the other, and then draw and arrow from the tail of one vector to the tail of the other vector (the net displacement vector)
-Use trigonometry to figure out the sides of the formed triangle (net displacement vector value)
how can we add two vectors as net displacement vector requires?
tan
opposite/hypotenuse
sin
cos
vector quantity because its specifications involves not only how fast an object is moving (its speed) but also the direction in which the object is moving
Is velocity an scalar quantity or vector quantity? why?
“velocity vector” that points in the direction of the object’s motion, and whose magnitude is the object’s speed

V
We represent the velocity of an object by a_
1. Note that the direction of the displacement vector is the direction of motion between successive points in the motion diagram. But the velocity of an object’s also points in the direction of motion, so an object’s velocity vector points in the same direction as its displacement vector
2. we’ve already noted that the magnitude of the velocity vector (how fast?) is the object speed
3. Because higher speeds imply greater displacements in the same time interval, you can see that the length of the velocity vector should be proportional to the length of the displacement vector between successive points on a motion diagram
*Consequently, the vectors connecting each dot of a motion diagram to the next, which we previously labeled as displacement vectors, could equally well be identified as velocity vectors
How can we draw the velocity vectors on the point motion diagram?
velocity vectors
displacement vectors can be replaced by_
change in path length divided by the corresponding change in time
speed
average property of the nonuniform motion over time interval (change s/change t)
average speed
For any moving body, the ratio of change of x/change of time, computed over shorter and shorter time intervals, eventually begins to approach a fixed a fixed numerical value, which we call the “limit” of the ratio. We define the instantaneous speed v to be this limiting value
Explain instantaneous speed
v= limit as change of t approaches zero of change of x/change of t
write the formula of instantaneous velocity
-scalar quantity
-It measures the rate of motion
speed is a scalar or vector quantity? what does it measure?
-vector quantity
-it gives direction of motion and as well as its rate
velocity is a scalar or vector quantity? what data does it give?
-displacement
-change of time
A body’s average velocity over a time interval is defined as its _divided by_
-name given to the vector that the average velocity approaches as the difference of t goes to 0
-instantaneous velocity is a vector tangent to the trajectory and having magnitude equal to the instantaneous speed
Describe the 2 characteristics of instantaneous velocity
-Instantaneous velocity gives both the direction of motion and the speed at an instant
what does instantaneous velocity gives? (2 information that gives)
we find that the velocity’s magnitude is very nearly the body’s instantaneous speed
when is calculated a body’s average velocity over a very short period of time interval, what happens?
instantaneous speed
the average velocity vector’s magnitude approaches the _as difference of t goes to 0
direction of the tangent to the trajectory
as the difference of t goes to 0, the direction of the average velocity vector approaches the _
-average velocity approaches instantaneous velocity
-a vector tangent to the trajectory and having a magnitude equal to the instantaneous speed
as difference of t (time) approaches 0, what happens? (2)
-V is related to the vector’s components by the Pythagorean theorem
V= square root of (Vx^2) plus (Vy^2)
how the components of velocity (Vx and Vy) are related with instantaneous speed? specify the formula
In the special case of uniform motion, a particle moves equal distances in equal time intervals, and so the ratio (difference of s/ difference of t) has the same value at any time interval. In this case, average speed is the same as instantaneous speed
How instantaneous speed relates with instantaneous velocity in the special case of uniform motion?
speeding up
slowing down
For one dimensional motion, an object changing its velocity is either _(2)
an object’s velocity (speed and direction) at an instant of time t
instantaneous velocity
average velocity
the position-vs-time graph slope is the _
greater
the position-vs-time graph for a racer is a curved line. The displacement (triangle x) during equal times gets_as the car speeds up
instantaneous velocity vx at time t= slope of position graph time t
formula of instantaneous velocity (within position vs time graph)
-we can compute a slope by considering a small segment of the graph
-Looking motion at an very small time interval, the slope appears to be constant
-Thus, make curved graphs appear straight by choosing a small enough time interval
-We can find the slope of the line by calculating the rise over the run. This would be the slope of the graph at the chosen small time interval, and thus the velocity at this instant time
How can we calculated the slope of a curved line (velocity changes)?
-The slope of the curve at a particular point is the same as the slope of a straight line drawn tangent to the curve at that point
*The slope of the tangent line is the instantaneous velocity at that instant of time*
When the slope of a curved line is the same as the slope of a straight line?
area under the curve in velocity vs time graph during time interval (triangle) t
In a velocity vs time graph, for an uniform motion, the displacement (change in x) is the _
-The velocity within each step (time interval) that has a constant velocity should be obtained by getting the area under the curve then add it to the other steps (time intervals) that have constant velocities different from the first step
-The total displacement of an object can be found as the sum of all the individual displacements during each of the constant-velocity steps
vf-vi= change in velocity= area under the velocity graph Vx between ti and tf
What you should do to get the displacement in a velocity vs time graph that the motion is not uniform? (include formula)
-straight-line motion in which equal displacement occur during any successive equal-time interval is called uniform motion or constant-velocity motion
-You must have equal displacements no matter how you choose your time intervals in uniform motions
Uniform motion (include its other name besides the definition)
straight line (could be diagonal)
straight horizontal line
The position vs time graph for an uniform motion is a _. the velocity vs time graph for an uniform motion is a_
an object’s motion is uniform motion if and only if its position vs time graph is a straight line
what is another definition of uniform motion that includes position vs time graphs?
slope of the graph
Vx= rise/run= change in x/ change in t= (Xf-Xi)/(tf-ti)
the object’s velocity Vx, along the x-axis can be determined (in uniform motion) by finding the _(include the formula)
Xf= Xi + Vx(triangle t)
what is the final position equation/ formula in an uniform motion case? (which only applies only to time interval during which the velocity is constant)
-slope of its position vs time graph
-area under the graph during time interval
we can deduce an object’s velocity by measuring the _graph. Conversely, if we have a velocity graph, we can get the displacement by getting the_

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