Unit 1.2 - Kinematics Flashcards
Displacement
The shortest distance from A to B along with direction
(The vector that corresponds to that distance)
Displacement unit
m
What’s the difference between displacement and distance?
Displacement has a positive and a negative, meaning they can cancel out
(Displacement is a vector)
Average speed
Total distance travelled divided by the total time taken
Instantaneous
In an instant
Instantaneous speed
The rate of change of distance
Speed unit
ms-1
Instantaneous speed on a graph
Gradient of the tangent of the distance-time graph at a given point
Average velocity
Total displacement travelled divided by the total time taken
Instantaneous velocity
The rate of change of displacement
Velocity unit
ms-1
Velocity on a graph
Gradient of the tangent on a displacement - time graph at a given point
Average acceleration
The change in velocity divided by the time taken for the change
Change in velocity
V - u
Instantaneous acceleration
The rate of change of velocity
Velocity unit
ms-2
Acceleration on a graph
Gradient of the tangent of the velocity-time graph at a given point
Symbol for displacement
x
How do we know if displacement is directly proportional to time on a graph?
Straight line through the origin
What does it mean if we have a straight one through the origin on a displacement-time graph?
Displacement is directly proportional to time
= the cars are moving at constant acceleration
When would we know if the cars are moving at constant acceleration on a displacement-time graph?
With a straight line through the origin that shows displacement is directly proportional to time
If a line is steeper than another on a displacement-time graph, what does it mean?
It has a higher constant velocity
What do we need to remember about the axes of the displacement-time graph?
As it’s a vector, it has both a positive and a negative
What does a flat line on a displacement-time graph tell us?
Gradient = 0
Velocity = 0
Body is stationary
When would we know that a body is stationary on a displacement-time graph?
With a flat line, as the gradient is zero, so the velocity is zero
What does a curve on a displacement-time graph show us in terms of proportions?
Displacement is increasing with time (a curve going up) but is not proportional to it
What does a gradient on a displacement-time graph show us?
Gradient = increasing and getting steeper (varying)
Rate of change of velocity = increasing
=accelerating
What does it mean that a gradient is varying?
Getting steeper
What would we see on a displacement-time graph to know that an object is accelerating?
A curve - gradient increasing
Velocity increasing
=acceleration
Velocity symbol
v
Which type of graphs are used to derive equations to describe the motion of objects that are subject to constant acceleration?
Velocity-time
What are velocity time graphs used for?
to derive equations to describe the motion of objects that are subject to constant acceleration (e.g - gravity)
Give an example of an object which is subject to constant acceleration
Gravity
What is gravity subject to?
Constant acceleration
What does a straight line through the origin of a velocity-time graph show?
That velocity is directly proportional to time
=Constant acceleration
How do we know if an object is in constant acceleration on a velocity-time graph?
Straight line through the origin = velocity is directly proportional to time
Type of graph for acceleration
Velocity-time
Type of graph for velocity
Displacement-time
What does it show us if a line is steeper than another on a velocity-time graph?
Higher constant acceleration
What do we need to remember when calculating acceleration on a velocity-time graph?
If the line goes down, use a negative in the equation
What does a flat line show on a velocity-time graph?
Gradient = 0
Acceleration = 0
Body moves at a constant velocity
What would show a body moving at a constant velocity on a velocity-time graph?
Flat line = gradient is zero
=Acceleration is zero
What do we need to remember about the axes of a velocity-time graph?
Have a positive and a negative - velocity is a vector
On which type of graph can we use the area under it to calculate the distance travelled?
Velocity-time
(and speed-time)
What does the area under a velocity-time graph show us?
Displacement
(NOT distance)
How do we calculate the distance travelled on a velocity-time graph?
Area underneath
What does a curve on a velocity-time graph show us?
(curve upwards)
Increasing gradient = increasing acceleration
Curve = not constant
What does the line on an acceleration-time graph show when throwing a ball into the air and why?
A straight, flat line at -9.81
Gravity, which is the force acting upon it, always acts downwards (negative) and is subject to constant acceleration
What does a velocity-time graph show when throwing a ball into the air and why?
A straight diagonal line that passes through the middle at t divided by 2
Straight line - gravity is constant
Negative displacement - travelling in the opposite direction
What does negative displacement show on a velocity-time graph?
Travelling in the opposite direction
What shows travelling in the opposite direction on a velocity-time graph?
Negative displacement
What shows travelling in the same direction on a displacement-time graph?
Journey up and down are the same after half way - mirror image
What would a displacement-time graph show when throwing a ball into the air and why?
A mirror image line, with the journey up and down the same after t divided by 2
The ball returned to its starting position - the journey up and down were the same
Gradient on a speed-time graph
Acceleration at any point
Area underneath a speed-time graph
Distance travelled
Acceleration symbol
a
What does a flat line on an acceleration-time graph represent?
Constant accleration
What represents constant acceleration on an acceleration-time graph?
A flat line
What can the direction of displacement be?
An angle
A bearing
“Up”, “down”
e.t.c…
What is a ball’s velocity at the top, just before falling?
Zero
When is a ball at its highest point?
When the velocity is zero
What type of graph do we use to derive equations of motion for uniform acceleration?
Velocity-time
What’s a velocity-time graph used for?
Deriving the equations of motion for uniform acceleration
What can the 4 equation of motion be used for?
Solving problems involving uniform acceleration
What type of acceleration can the equations of motion be used for?
Uniform acceleration
Uniform acceleration
An object’s velocity increasing at a constant rate
An object’s velocity increasing at a constant rate
Uniform acceleration
x symbol meaning
Displacement
Displacement symbol
x
u symbol meaning
Initial velocity
Initial velocity symbol
u
Final velocity symbol
V
V symbol meaning
Final velocity
Acceleration symbol
a
a symbol meaning
Acceleration
t symbol meaning
Time taken
Time taken symbol
t
Explain how the v = u + at equation of motion is derived
the gradient of the velocity-time graph gives us acceleration
(Gradient = change in y
—————
change in x)
gradient = a = v-u
——
t
(re-arrange)
v = u + at
Explain how the x = ut + 1/2 at^2 equation of motion is derived
the area under the graph gives us displacement
Displacement = x = x = ut + 1/2 (v-u)t
We know from v = u + at that (v-u) is equal to at so…
x = ut + 1/2(at)t
x = ut + 1/2 at^2
Explain how the x= 1/2(u+v)t equation of motion is derived
The graph shows constant acceleration, so the mean velocity is half the maximum velocity (midway point on the graph)
(the two triangles on either side of the newly drawn line are the same, so we can just workout the area underneath the line!)
Mean = total of values
———————
How many values there are
Area under green line
x = (v+u t
——
2)
(rearrange)
x = 1/2 (u+v)t
Explain how the v^2 = u^2 + 2ax equation of motion is derived
Derived from equation 1 and 3 (eliminating the term t, time)
v = u + at
(make t the subject)
(v-u
—— = t.
a).
So, we can put this instead of the t in the other equation
x = 1/2 (u + v)t
1/2 (u+v) x (v-u = x
——
a)
x = (u+v)(v-u) FOIL
————
2a
x = uv -u^2 + v^2 -uv
————————
2a
x = -u^2 + v^2\
—————
2a
2ax = -u^2 + v^2
V^2 = u^2 + 2ax
When using the equations of motion, what do we need to do?
Pick the equation that doesn’t have the first unknown we want to work out in it, then choose another one for the other (try to avoid the quadratic one)
What do we need to remember to do in a calculation involving the ut+1/2at^2 equation?
Square the half too - put it all in the calculator at once, without brackets!
If an object is falling, what is its acceleration?
9.81ms-1 (gravity)
If an object is hovering, what’s its initial velocity?
0
When is acceleration to be written as 9.81?
when an object is falling, without air resistance (vertical component)
Which equation of motion do we try to avoid using and when is it easiest to use?
x = ut + 1/2 at^2
(Unless u=0 - it then cancels the first bit out and it’s easy)
Under what conditions is the object when we compare the affects of air resistance on it?
In a uniform gravitational field
When and what is the force acting upon an object without air resistance?
Moving up, at the highest point, or moving down
the weight of the body (W) is the only force acting upon it
What does an object experience without air resistance and why?
Constant acceleration, as the weight of the body is the only force acting upon it
Under what conditions does an object experience constant acceleration and why?
Without air resistance, as weight is the only force acting upon the object
Under which conditions is weight the only force acting upon an object?
Without air resistance
Describe the gradient of the velocity-time graph when an object is moving without air resistance
Constant throughout its rise and fall
Under which conditions is the gradient of a velocity-time graph constant throughout its rise and fall?
Without air resistance
What is an object undergoing if an object is moving without air resistance?
Free fall
When isn object undergoing free fall?
When the gradient of the velocity-time graph is constant throughout its rise and fall, when an object moves without air resistance
Which factors reduce acceleration?
Air resistance
Friction
What do both air resistance and friction do?
Reduce acceleration
What can we visually see that happens to an object when its thrown in the air and air resistance acts upon it?
It travels less far
Under which conditions does an object travel less far when thrown?
With air resistance
What are air resistance and friction forces against?
The direction of the object
What are the forces against the direction of an object?
Air resistance
Friction
Describe the line on a velocity-time graph when an object moves with air resistance
No longer a straight line
Gradient starts steep and flattens
Describe the line of a graph when an object moves…
i.) without air resistance
ii.) with air resistance
i.) Gradient is constant throughout its rise and fall
ii.) Not a straight line - gradient starts steep and eventually flattens
When an object rises with air resistance, what are the forces acting upon it and in which direction?
Air resistance and weight, downwards
Under which conditions do both air resistance and weight act on a body and at which stage in its motion?
With air resistance, as it moves upwards
What does the fact that both air resistance AND weight act downwards on a body as it moves upwards mean for its speed?
Speed decreases at a rate faster than 9.81ms-2
When does the speed of an object decrease at a rate faster than 9.81ms-2?
When an object moves upwards WITH air resistance
Compare the time taken to reach maximum height when an object moves
i.) without air resistance
ii.) with air resistance
i.) longer time
ii.) shorter time
Compare the maximum height reached when an object moves
i.) without air resistance
ii.) with air resistance
i.) higher
ii.) lower
What happens at the highest point to an object moving with air resistance acting upon it?
The body is momentarily at rest
Air resistance is zero
The only force is weight, so the acceleration i 9.81ms-2
At which point is an object momentarily at rest when travelling upwards?
At the highest point
What state is an object in when at its highest point?
Momentarily at rest
When is the air resistance acting upon an object moving upwards zero?
At the highest point
What’s the air resistance of an object at its highest point?
0
When is the only force of an object its weight if its moving with air resistance acting upon it?
At the highest point
What is the acceleration of an object at its highest point?
9.81ms-2
At which point is the acceleration of an object 9.81ms-2?
At its highest point
When does air resistance oppose a body’s weight?
As it falls
What does air resistance do to a body as it falls?
Opposes its weight
Describe the acceleration of an object when moving downwards (with air resistance)
Less than 9.81ms-2
When is the downwards acceleration of an object less than 9.81ms-2?
As it falls, and the air resistance opposes its weight
What does air resistance increase with?
Speed
What does speed do to acceleration?
Increases it
When would there be no resultant force for a falling object?
When the air resistance has increased with speed to equal weight in the opposite direction
What happens when the air resistance has increased with speed to equal weight in the opposite direction?
There’s no resultant force, so the object falls at a constant speed (terminal velocity)
What causes an object to fall at a constant speed?
Having no resultant force - air resistance equals weight in the opposite direction
What causes an object to have no resultant force?
Air resistance has increased with speed to eventually equal weight in the opposite direction
What speed is an object moving at at terminal velocity?
Constant speed
What is an object moving at once it’s reached a constant speed when falling?
Terminal velocity
What do we have to do if we receive discrete ration when using the equations of motion?
Input it as a negative value
Under which conditions can we apply the equations for uniformly accelerated motion to falling bodies?
Without/ignoring air resistance
What does every object on Earth have and why?
A weight due to the force of gravity
What’s the velocity of a ball when it’s at its highest point?
0ms-1
In which direction does air resistance always act?
Opposes the direction of motion
What fact makes everything a lot easier when dealing with projectile motion?
Vectors that are perpendicular or horizontal are independent of each other
So, we can use them separately when making calculations
What is the only force acting on a ball flying through the air when undergoing projectile motion?
Gravity
Describe the relationship between perpendicular and horizontal vectors
Independent of eachother
For a ball during projectile motion, what is its vertical…
i.) velocity
ii.) acceleration
i.) slows down, then speeds up - becomes negative
ii.) g (9.81ms-2)
For a ball during projectile motion, what is its horizontal…
i.) velocity
ii.) acceleration
i.) the same
ii.) zero
What two things do we have in common for calculations involving projectile motion?
- The time for the object to reach maximum height is this same as half the total flight time (vertically and horizontally)
- The equations for motion for the horizontal part are simple - there’s no acceleration so Vh = Xh divided by tH and tH is the same as (2 x tv)max height
What’s the time for an object to reach maximum height during projectile motion? Which direction is this?
The same as half the total flight time
Horizontally and vertically
What are the equations of motion for the horizontal part during projectile motion?
Vh = xh divided by th (horizontal velocity = horizontal displacement divided by horizontal time)
tH = (2 x tv)max height
(The total time taken, horizontally is equal to twice the time taken vertically to reach the maximum height)
Why are the equations for the horizontal part simple during projectile motion?
Is has no acceleration
Which vector uses the simplest equations of motion with projectile motion and why?
Horizontal as there’s no acceleration
How do you work out the vertical and horizontal components from an initial velocity during projectile motion?
Trigonometry
Where does Xv go on the projectile motion graph?
A straight vertical line down the centre
At which point is Vv = 0 during projectile motion?
At the highest point
What is Vv at the highest point during projectile motion?
0ms-1
When would acceleration be a negative value when calculating with projectile motion?
When it foes to the opposite direction of our positive acceleration
What do we need to remember to do if calculating the total time during projectile motion?
Calculate the time to the halfway point (using equations of motion vertically)
Multiply by 2 for the total time
Range
Total horizontal distance
Word for total horizontal distance
Range
What do we need to remember when calculating the range of a ball undergoing projectile motion?
The speed was the same throughout, therefore Vh is the same as Uh
We can then use some equations
If a ball is being dropped, for example, as our projectile motion, what do we do with our acceleration?
It’s easier to make the downwards acceleration positive as we only have one direction
Initial velocity vertically from dropping
0ms-1
Which vector’s initial velocity is zero when dropping an object?
Vertical
Do we need to double the time if working out the time taken for a ball to drop?
No - it’s only going down
Is velocity a force?
No
How do vertical and horizontal times compare in a question where something is falling?
The same - it takes the same time to go down as it does to go up
In what type of question is the horizontal and vertical time the same?
When just falling
How would the maximum height a ball reaches be different on Earth than on the moon and why?
Lower on Earth
-Stronger force of gravity exists on Earth - reduces the flight time, the max height and range
-Air resistance also reduces it
Which factors affect the maximum height a ball could reach on Earth?
Air resistance
Force of gravity
What does gravity affect on a ball?
Reduces flight time, max height and range
What do both gravity and air resistance affect on a ball?
Its maximum height reached
Why are perpendicular directions chosen for resolving vectors?
-Need right angled triangles for trigonometry
-Vectors that are perpendicular are independent on each other
What type of vectors are independent of each other and form right angled triangles and what does this mean for them?
Perpendicular = they’re chosen for resolving vectors
What does the area underneath an acceleration time graph represent?
Change in velocity
Is there air resistance in space? Why?
No
No atmosphere
No air
No air resistance
What would happen to the time of flight if the horizontal velocity were increased? Why?
No effect - time of flight depends on the vertical velocity
What does the time of flight depend on?
Vertical velocity, not horizontal
What does vertical velocity impact that the horizontal velocity doesn’t?
The time of flight
What do we need to remember when re-arranging x=ut+1/2at^2 equation to get t?
Divide by the 9.81 and then the 1/2 afterwards
Under which conditions could acceleration by particularly large?
When occurring over a small duration
Describe acceleration when occurring over a small duration
Can be particularly large
Does something have a horizontal velocity when it falls?
Yes
What’s the opposite of 1/2 for the x=ut+1/2at^2 equation?
x2
What does a projectiles flight time depend on?
-drop height
-(initial) vertical velocity
-acceleration due to gravity
What is terminal velocity?
When the resistive forces are equal to the weight of the object, giving zero resultant force
What is meant by undergoing free-fall?
When the weight of the body is the only force acting on it (force of gravity) and resistive forces are negligible
What do you do with velocity if it’s in the opposite direction?
Negative velocity
Why is the horizontal acceleration of a projectile zero throughout?
Gravity acts vertically = no forces
Give an example of a situation with a changing velocity but a constant speed
Circular motion with a constant speed
What do we need to remember about the kinematic equations of an object is decelerating?
It should be a negative value
What do we do to identify N3 pairs?
- Type of force (same for both)
- Use the definition, inputting “object A” and “B” with those in the question
What does air resistance do to the acceleration of a falling object?
It’s less than 9.81ms^-2
When is velocity negative?
When an object is moving backwards
