Chapter 2-ID Kinematics
When an object's velocity is zero, does its acceleration have to be zero?
-NO! -an objects velocity cannot stay at zero, it must pass through it
Can you be at rest and still have an acceleration?
-YES! -acceleration can be negative or positive -you won't be staying at rest for very long
What is acceleration equal to when velocity is constant?
-ZERO
What is kinematics?
-a description of motion
As such, what is the only thing that distances have associated with them?
-a numerical value
What mathematical problem/hitch does equation number three pose?
-a positive and a negative value can be obtained for final velocity
What are the constant acceleration equations?
-a set of equations that govern the kinematics of constant acceleration
What is a position vector?
-a value that has a numerical value and a direction, where the tail of the vector is at the origin and the head is at the location of the object
Do acceleration and velocity have the same sign? Opposite signs?
-acceleration and velocity may have the same or opposite signs
On an acceleration versus time graph, what do we know if acceleration is greater than 0? In terms of a, v, and x?
-acceleration is positive -velocity may be positive or negative -object may be moving in a positive or negative x direction
When an object is travelling "down," what will gravity do?
-adds 9.81 m/s to its velocity every second
(Provided what can be ignored)?
-air resistance
Where is the head of a displacement vector located?
-at the final location of an object
Where is the head of a position vector located?
-at the final location of an object
Where is the tail of a displacement vector located?
-at the initial location of an object
What does the slope of a velocity vs. time graph represent?
-average acceleration
What does this mean?
-average speed will be greater than or equal to average velocity
What values can average velocity have?
-average velocity can be positive, negative, or zero
Why specifically is average speed always positive?
-because both distance and elapsed time are positive
Why?
-because d≥ |Δx| (delta x with a hat)
Why is average velocity used more frequently than average speed?
-because it provides us the direction that the object is moving in
Why not?
-because speed is scalar and velocity is a vector
Why is time up equal to time down?
-because the same acceleration is governing the motion of the object
What values can acceleration have?
-can be positive, negative, or zero
What does the area under an acceleration vs. time graph represent?
-change in velocity, ∆v
When an object is travelling "up," what will gravity do?
-chips away 9.81 m/s from its velocity every second
The sign of what will be matched by the sign of the average velocity?
-displacement
How does distance differ from displacement?
-displacement accounts for the "net effect" of the trip, and throws away all details -however, distance accounts for "every stop along the way
What does the area under a velocity vs. time graph represent?
-displacement, ∆x
What does "near the surface of Earth" mean exactly?
-equal to anywhere you will go in your entire lifetime (except if you travelled into space) -everyday conditions
When can g not be used?
-if an object is held in place by hand or other tool -if an object has hit the ground (or otherwise been stopped) -if air resistance is not negligible
Can the final velocity in the y direction of an object be equal to zero when an object hits the ground?
-no it cannot, because gravity is imposing a constant acceleration on an object -for this reason, final velocity is assumed to be the moment right before an object hits the ground
When acceleration is constant, does it ever change direction? Why or why not?
-no it does not, because it is constant -it is only velocity that changes direction
If average speed is scalar, does it have a (+) or a (-) sign associated with it?
-no it does not, it is always positive
Are average speed and average velocity the same thing?
-no they are not
Can distance have a (+) or a (-) sign associated with them?
-no they cannot
Is displacement origin dependent? Why or why not?
-no, displacement is not origin dependent -a result of the fact that displacement is calculated using two points, neither of which are at the origin
Does acceleration have to be continuous? Why or why not?
-no, it does not have to be continuous -one can change the instructions to velocity instantaneously
Is gravity necessarily negative? Why or why not?
-no, it is not necessarily negative -it is dependent upon the mathematical scaffolding that is setup
Does velocity increase uniformly with a positive acceleration?
-not necessarily
How many dimensions are associated with acceleration?
-one dimension
How many dimensions are associated with displacement?
-only one
How many dimensions are associated with velocity?
-only one
When can gravity be used?
-only when an object is near the surface of Earth
What are the two different types of kinematics?
-scalar and vector
What is the only difference between instantaneous speed and instantaneous velocity?
-speed will always be positive, while velocity can be positive, negative, or zero
What does a negative slope on a velocity versus time graph indicate?
-that acceleration is negative -object is decreasing the velocity at which it travels over time
What does a positive slope on a velocity versus time graph indicate?
-that acceleration is positive -object is increasing the velocity at which it travels over time
What does a zero slope on a velocity versus time graph indicate?
-that acceleration is zero -the velocity at which an object is traveling remains constant
On a velocity versus time graph, what do we know if velocity is less than zero?
-that movement of the object is in the negative x direction
On a velocity versus time graph, what do we know if velocity is greater than 0?
-that movement of the object is still in the positive x direction
On a velocity versus time graph, what do we know if velocity is equal to zero?
-that the object is at rest
What does a zero slope on a position versus time graph indicate?
-that velocity is equal to zero -object is stationary
What does a negative slope on a position versus time graph indicate?
-that velocity is negative -object is travelling in a (-) x direction over time
What does a positive slope on a position versus time graph indicate?
-that velocity is positive -object is travelling in a (+) x direction over time
What does the area underneath a position vs. time graph represent?
-the area under the graph does not represent anything physical
What is gravity?
-the constant force of acceleration on objects in free fall
What does the average velocity tell us?
-the direction that an object is moving in
Suppose that we are measuring the movement of the object in seconds. If negative acceleration is applied to a positive velocity, will the distance covered during the first second of negative acceleration be greater than or less than the distance covered during the second second of negative acceleration?
-the distance covered during the first second will be greater
If average velocity is less than zero, what direction does the object move in?
-the negative direction
If average velocity equals zero, what direction does the object move in?
-the object is stationary, so it does not move in the positive or negative direction
What is the effect on an object when velocity is negative and acceleration is positive?
-the object will slow down as acceleration "chips away" at its speed and negative velocity -eventually the object will come to a complete standstill, then will begin to travel with greater velocity in the positive direction -->first, the acceleration chips away at the velocity, then, acceleration adds to the velocity
What is the effect on an object when velocity is positive and acceleration is negative?
-the object will slow down as acceleration "chips away" at its speed and positive velocity -eventually, the object will come to a complete standstill, then will begin to travel with greater velocity in the negative direction -->first, the acceleration chips away at the velocity, then, the acceleration adds to the velocity
What is the tail of a position vector always tied to?
-the origin
If average velocity is greater than zero, what direction does the object move in?
-the positive direction
What is the definition of acceleration?
-the rate of change of velocity over time -how many meters per second the velocity changes by every second -the set of instructions that tells the velocity how to change with time -how acceleration evolves over time
What is instantaneous speed?
-the speed of an object at an isolated, small increment of time
What is the effect on an object when acceleration and velocity have the same sign?
-the speed of the object increases -the velocity of the object increases in the (+) direction
What is the effect on an object when velocity is negative and acceleration is negative?
-the speed of the object increases -the velocity of the object increases in the negative direction
What is instantaneous velocity?
-the velocity of an object at an isolated, small increment of time
When an object is released from a hand or a vessel (such as a hot air balloon), what is its velocity?
-the velocity of the object is the same as the velocity of the hand or vessel from which it was reelased
What two important things can be assumed for a ground level flight?
-time up is equal to time down -velocity final = (-)velocity initial
What are the two methods that can be used to calculate average speed?
-use distance / Δ time -average all instantaneous speeds to find average speed, using time averages
How then, do you determine if final velocity is positive or negative?
-use intuition -if an object is travelling downward, then final velocity cannot be positive
What are the two methods that can be used to calculate average velocity?
-use ∆x/∆t -average all instantaneous velocities to find average velocity, using time averages
How is acceleration calculated in this case?
-using rise/run -rise/run = ∆v/∆t = (v final-v initial)/(t final-t initial)
How is velocity calculated in this case?
-using rise/run -rise/run = ∆x/∆t = (x final-x initial)/(t final-t initial)
What does the slope of a position vs. time graph represent?
-velocity
When an object is in a flight with positive y displacement, what is its velocity when it as at the top of its motion? Why?
-velocity is equal to zero -it is changing direction, moving from a positive upwards flight to a negative downwards flight
When are instantaneous acceleration and average acceleration the same?
-when acceleration is constant
When does velocity increase uniformly with a positive acceleration?
-when acceleration is constant
When does velocity not increase uniformly with a positive acceleration?
-when acceleration is not constant
When should these equations never be applied?
-when acceleration is not constant
What is a ground level flight?
-when an object enters and exits flight at the same height
When are instantaneous speed and velocity the same?
-when velocity is constant
Can vectors have a (+) or (-) sign associate with them?
-yes
Is acceleration a vector?
-yes -it has both a magnitude and a direction
Does velocity have to be continuous? Why or why not?
-yes it has to be continuous -if you want to move from one velocity to the other, you must pass through all intermediate velocities
Can acceleration be negative and movement in the x direction be positive?
-yes, if velocity is still positive
Does position have to be continuous? Why or why not?
-yes, it has to be continuous -if you want to move from one position to the other, you must pass through all intermediate positions
Do displacements have a (+) or a (-) sign associated with them?
-yes, they do
What is average speed equal to?
Average speed = distance / Δ time
What is average velocity equal to?
Average velocity = ∆x/∆t = (x final-x initial)/(t final-t initial)
How are average velocity and average speed related to each other?
average speed ≥ |average velocity|
As such, how do distance and displacement typically compare numerically?
d≥ |Δx| (delta x with a hat)
What is the relationship between instantaneous speed and velocity?
instantaneous speed = |instantaneous velocity|
What mathematical symbol denotes position vector?
x with a hat
If the tail of a displacement vector is at the initial location of an object and the head is at the final location of an object, how is Δx calculated?
Δx = final position - initial position Δx = xf - xi
What mathematical symbol denotes displacement vector?
Δx with a hat
What is the mathematical expression of acceleration?
∆v/∆t = (v final-v initial)/(t final-t initial)
