Week 2 - Chapter 2 - Kinematics Flashcards
What is defined as the study of motion without considering causes?
Kinematics
The word “kinematics” comes from a Greek term meaning motion and is related to other English words such as “cinema” (movies) and “kinesiology” (the study of human motion).
What is the simplest type of motion aka one-dimensional kinematics?
Motion along a straight line, or one-dimensional motion
In order to describe the motion of an object, what must you be first able to describe?
Its position; where it is at any particular time.
What is a change in position known as?
Displacement which implies that an object has moved, or has been displaced.
Concept Review
▲x = displacement, xf = final position, x0 is the initial position
▲x = xf - x0, this is the change in position of an object
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What does ▲(delta) always mean within the text?
“change in” whatever quantity follows it; thus, ▲x means change in position.
This is always solved by subtracting the initial position from the final position; xf - x0 = ▲x
Note that the SI unit for displacement is the meter (m), but sometimes kilometers, miles, feet, and other units of length are used. Keep in mind that when units other than the meter are used in a problem, you may need to convert them into meters to complete the calculation.
For x, it is “the location relative to the reference frame” (i.e., airplane, earth, etc.)
What does displacement have?
A direction AND magnitude.
In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you are free to select positive as being any direction).
What is distance defined as?
It is defined as the magnitude or size of displacement between two positions and has no direction.
For example, the professor’s ▲x = +2.0m (displacement)
For distance of what the professor walks = 2.0 m (distance is magnitude only with no sign)
Explain how distance or magnitude of displacement can be different than “distance traveled.”
For the professor problem, he could walk back and forth in front of the whiteboard accumulating 150 m traveled yet he may only have a magnitude of displacement from his starting position of 2 m.
For example, the professor could pace back and forth many times, perhaps walking a distance of 150 m during a lecture, yet still end up only 2.0 m to the right of her starting point.
In this case her displacement would be +2.0 m, the magnitude of her displacement would be 2.0 m, but the distance she traveled would be 150 m.
In kinematics we nearly always deal with displacement and magnitude of displacement, and almost never with distance traveled. One way to think about this is to assume you marked the start of the motion and the end of the motion. The displacement is simply the difference in the position of the two marks and is independent of the path taken in traveling between the two marks. The distance traveled, however, is the total length of the path taken between the two marks.
What is displacement and distance an example of when it comes to quantities?
Displacement is an example of vector quantity.
Distance is an example of a scalar quantity.
Since displacement is an example of a vector quantity, what is a vector quantity?
How do you annotate a vector in one-dimensional motion?
A vector is any quantity with both magnitude and direction. Other examples of vectors include a velocity of 90 km/h east and a force of 500 newtons straight down.
With a + or -
Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector’s magnitude (e.g., the larger
the magnitude, the longer the length of the vector) and points in the same direction as the vector.
Since distance is an example of a scalar quantity, what is a scalar quantity?
A scalar is any quantity that has a magnitude, but no direction. For example, a 20 degree Celsius temperature, the 250 kilocalories of energy in a candy bar, a 90 km/h speed limit, a person’s 1.8m height, and a distance of 2.0 m are all scalars–quantities with no specified direction.
Note: A scalar can be negative, such as -20 degrees Celsius temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented with arrows.
What does every measurement of time involve?
A change in some physical quantity.
In physics, time is change or the interval over which change occurs.
Concept Review
▲t = elapsed time, tf = is the time at the end of motion, t0 = is the time as the start of motion.
▲t = tf - t0, this is the change in time or elapsed time
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What is average velocity and how is it calculated?
Average velocity is displacement (change in position; vector quantity) divided by the time of travel. See photo.
Notice that this definition indicates that velocity is a vector because displacement is a vector. It has both magnitude and
direction. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph),
and cm/s, are in common use.
What does average velocity not tell us?
Average velocity of an object does not tell us anything about what happens to it between the starting point and ending point. To get more details, we much consider smaller segments of the trip over smaller time intervals.
What is the average velocity at a specific instant in time (or over an infinitesimally small time interval)?
Instantaneous velocity v
What does speed have that velocity does have?
Speed as no direction thus speed is scalar
(V for velocity and vector; S for speed and scalar)
What must we distinguish about speed that we already distinguish about velocity?
Average and instantaneous speed
What is instantaneous speed?
It is the magnitude of instantaneous velocity. (DUH)
Since instantaneous speed is instantaneous velocity with no direction, how does average speed differ from average velocity?
Average speed is the DISTANCE TRAVELED divided by elapsed time. Average speed can be greater than average velocity because, if you remember, distance traveled encompasses all travel summed together while magnitude of displacement if starting point subtracted from final destination.
Remember: average velocity is change in position relative to its environment divided by the time of travel.
Scenario for average velocity and average speed (No answer)
For example, if you drive to a store and return home in half an hour, and your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero, because your displacement for the round trip is zero. (Displacement is change in position and, thus, is zero for a round trip.) Thus average speed is not simply the magnitude of average velocity.
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What is the definition and equation of average acceleration?
It is the RATE at which velocity changes.
Why is average acceleration SI units in meters divided by seconds squared?
Since acceleration is velocity in m/s divided by time in seconds.
This means meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.
Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.
Review: When is acceleration present?
When there is a change in either magnitude (increase or decrease in speed) or in direction (the quicker the turn, the greater the acceleration)
Acceleration is a vector in the same direction as the change in velocity, ▲v. Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.
What caveat is important to remember when keeping in mind that acceleration is in the direction of the change in velocity?
It is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration.
What does deceleration always refer to?
It refers to acceleration in the direction opposite to the direction of velocity.
Deceleration always reduces speed. Negative acceleration, however, is acceleration in the negative direction in the chosen coordinate system.
Negative acceleration may or may not be deceleration, and deceleration may or may not be considered negative acceleration.
See image for details.
Properly label the acceleration in respect to its coordinate system.
a - Positive or negative acceleration and why?
b -
c -
d -
a - The car is speeding up as it moves to the right therefore, it has positive acceleration in our coordinate system.
b - The car is slowing down as it moves to the right. Therefore, it has negative (left on the x axis) acceleration in our coordinate system, because its acceleration is toward the left. This is deceleration because the direction of acceleration is opposite to its direction of motion.
c - The car is moving toward the left, but slowing down over time. Therefore, its acceleration is positive in our coordinate system because it is toward the right. However, the car is decelerating because its acceleration is opposite to its motion.
d - This car is speeding up as it moves towards the left. It has negative acceleration because it is accelerating toward the left. However, because its acceleration is in the same direction as its motion, it is speeding up (not decelerating).
What is instantaneous acceleration a?
It is the acceleration at a specific instant in time, and is obtained by the same process as discussed for instantaneous velocity, that is, by considering an infinitesimally small interval of time.
Kinematics Consolidated Review
- Establish position, more precisely specify position relative to a convent reference frame.
- Displacement is the CHANGE IN POSITION of an object | ▲x = xf - x0 | SI = meters (m) | Displacement has magnitude AND direction. (vector)
- Distance Traveled is the TOTAL LENGTH OF THE PATH TRAVELED BETWEEN TWO POSITIONS | |▲x| = xf + x0 + … | Distance Traveled has magnitude ONLY. (scalar)
- Distance is the MAGNITUDE OF DISPLACEMENT BETWEEN TWO POSITIONS | |▲x| = xf +x0 | Distance has magnitude ONLY. (scalar)
- Time is change, or the interval over which change occurs.
- Elapsed time is the difference between the ending time and beginning time | ▲t = tf - t0 | Motion starts at time equal to zero (t0 = 0) for simplicity. The symbol t is used for elapsed time unless otherwise specified (▲t = tf = t)
- Average velocity is displacement (change in position) divided by the time of travel (See flipside for formula) | SI = m/s | Vector quantity because displacement of x is a vector quantity.
- Instantaneous velocity v is the average at a specific instant in time (or over an infinitesimally small time interval)
- Average speed is the distance traveled by elapsed time (See flipside for formula) | SI = m/s | Scalar quantity because distance is a scalar quantity.
- Instantaneous speed s is the MAGNITUDE ONLY of instantaneous velocity.
- Acceleration is the greater change in velocity over a given time.
- Average acceleration is the rate at which velocity changes. It is the change in velocity divided by the change in time (See flipside for formula) | SI = m/s^2 (literally means by how many meters per second the velocity changes every second). |
- Acceleration is a vector in the same direction as the CHANGE in velocity, ▲v. Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.
- Acceleration may be in the direction of the change in velocity, but not necessarily always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of motion. This is known as deceleration.
What does the m/s^2 mean when dealing with acceleration? When is acceleration present?
Literally means by how many meters per second the velocity changes every second. When the object changes in magnitude or direction.
