Chapter 7 Flashcards
What is displacement
The distance in a given direction
Speed
The defund as change of distance per unit time
Velocity
The defined as change of displacement per unit time. In other words velocity is speed in a given direction.
Speed equation
Speed = s / t
Speed = v Distance = s Time = t
Distance travelled
S = v x t
Instantaneous speed
Tangent speed at an instant in time.
Average Speed
Straight line from start to end
Speed over a period of time
Y axis distance
X axis time
Distance = s
Time = t
S₂ - S₁ / T₂ - T₁
Average speed = S/T
Circular motion
In a circular motion speed is constant but as the direction is always changing V is always changing
So we say that the object is accelerating
Acceleration is defined what?
Defined as the change of velocity per unit time
Unit of acceleration
Ms-²
Acceleration equation
Change of velocity / time taken
V-U / T
Rearrange
V = u+ AT
Non uniform acceleration
Non uniform acceleration is where the direction of motion of an object changes or it’s speed changes at a varying rate.
Acceleration = gradient of the line on the velocity-time graph
Final velocity measurement
Ms - ¹
Initial velocity
Ms -¹
Time
Seconds
Velocity time graph
Slope which goes down straight diagonal
Acceleration from a V-T graph
Curve graph which needs a tangent
V2 - V1 / T2 - T1
Displacement from a V-T graph
Triangle and rectangle boxes
S= (1/2 x t1 x v1) + ((t2-t1) x v1)
Suvat equation
Without S
V= u + at
Suvat equation
Without A
S= u+v/2 x t
Average velocity
U+V/2
Suvat equation
Without V
S= u x T + (1/2) x a x T² Rearrange to find T √S / a x 1/2 = T Rearrange to find S S= u x T + 1/2 x 9.8 x (0.9²)
Suvat equation
Without u
S= v x T - (1/2) x a x T²
Suvat equation
Without T
V² = u² + 2 x a x s
Weight = what?
Mass x gravity
Force = what?
Mass x acceleration
Newtons second law
Free fall info
Heavy objects typically fall faster in air vac use air resistant = cross sectional area = r²
Weight = mass = volume = r³
Distance time graph
Wave going up then down then up
Like a transverse wave but going up
Displacement time graph
Goes up then down like a shape of a hill
Speed time graph
V shape graph that is a straight line
Example
Going from 10 on the y axis to 0 on the y axis and then going back up in a straight line but NOT virtual diagonal line
Velocity time graph
Y axis going from POSITIVE to NEGATIVE a straight line down diagonally
What happens to distance
If distance increases with time as there isn’t really any such things as negative distance due to its scalar nature
Why does displacement end at zero
It ends a zero due to its vector nature. This plots a similar parabola y = -ax² + bx + c
Why does velocity have a constant negative gradient
This is because of -9.81 ( gravity) and the displacement when v>0 = displacement when v<0 ( area under line)
Speed time graph
Gradient = what ??
Velocity
Δy/Δx =Δs/T = velocity
Velocity time graph
Gradient = what ??
Area = what ??
- Acceleration
- displacement
Δy/Δx = Δv/T = acceleration
Y x X = v x T = displacement
Projectile motion
Projectile motion = horizontal motion + vertical motion
Projectile motion info 1
Horizontal place we simply use v=s/T as there is no acceleration
Vertical plane
Treated as a free fall question
Example question
Vertical = Suvat Horizontal = v=s/T So for horizontal you need the horizontal line from the triangle and the Suvat answer Suvat = T Horizontal = s
Constant speed of a circle
V = 2 x π × r / T
Where T is the time to move round once and 2 x π x r is the circumference of the circle.
Acceleration is defined …
As charge of velocity per unit time
Uniform acceleration
Uniform acceleration is where the velocity of an object moving along a straight line changes at a constant rate. In other words the acceleration is constant.
A= v-u / t V = initial U = final
Constant velocity
Speed y axis
Time x axis
When an object is moving at a constant velocity.
S = v x t
Straight line horizontal
Constant acceleration
Speed = y axis Time = x axis
Consider an object at constant acceleration (a) from initial velocity (u) to velocity (v) at time (t)
Equation = s= (u+v) x t / 2 (Suvat equation )
Graph
Diagonal line from lowest point on y axis to the highest point on x axis
Middle of y axis is the average speed
Changing acceleration
When an object is changing acceleration, let v represent the velocity at time t and (v+δv)
(δ = delta )
Represent the velocity a short time later at (t+δt).
Graph
So it’s a (s) graph but the (s) is horizontal
V+δv is above v
So is the same with time
Displacement = area under the line of velocity time graph
Example like a constant velocity
Area = (6 y axis) x (5 x axis) = 30m
Distance = 30m
Does a heavy object fall faster than a lighter object.
Release a stone and a small coin at the same time. Which one hits
ine ground first? The answer to this question was first discovered by
calileo Galileli about tour centuries ago. He reasoned that because any
number of identical objects must fall at the same rate, then any one
such object must tall at the same rate as the rest put together. So he
concluded that any two Objects must fall at the same rate, regardless
of their relative weights.
The difference between distance - time graph and a displacement - time graph
Part 1
Displacement is distance in a given direction from a certain point.
Consider a ball thrown directly upwards and caught when it returns.
If the ball rises to a maximum height of 2.0 m, on returning to the
thrower its displacement from its initial position is zero. However, the
distance it has travelled is 4.0 m.
Graph Semi circle graph Y axis = displacement X axis = time Highest point is the maximum point
Immediately after leaving the thrower’s hand, the velocity is
positive and large so the gradient is positive and large.
As the ball rises, its velocity decreases so the gradient decreases.
At maximum height, its velocity is zero so the gradient is zero.
As the ball descends, its velocity becomes increasingly negative,
corresponding to increasing speed in a downward direction. So the
gradient becomes increasingly negative.
The difference between distance - time graph and a displacement - time graph
Part 2
Distance graph
The distance travelled by the object changes with time as shown
by Figure 2. The gradient of this line represents the speed. From
projection to maximum height, the shape is exactly the same as in
Figure 1. After maximum height, the distance continues to increase so
the line curves up, not down like Figure 1.
Graph
Y axis = distance
X axis = time
First half of the graph slowly projects upwards then the second half it projected further upwards
Half way of the graph before being projected upwards half way is the maximum height
Looks like a horizontal (s).
The difference between speed - time graph and a velocity - time graph
Part 1
Velocity is speed in a given direction. Consider how the velocity of
an object thrown into the air changes with time. The object’s velocity
decreases from its initial positive (upwards) value to zero at maximum
height then increases in the negative (downwards) direction as it falls.
The difference between speed - time graph and a velocity - time graph
Part 2
1
The gradient of the line represents the object’s acceleration
This is constant and negative, equal to the acceleration ot free fall, q.
The acceleration of the object is the same when it descends as when
it ascends so the gradient of the line is always equal to -9.8 ms-2
2
The area under the line represents the displacement of the
object from its starting position.
The area between the positive section of the line and the time
axis represents the displacement during the ascent.
The area under the negative section of the line and the time
axis represents the displacement during the descent.
Taking the area for a as positive and the area for b as negative, the
total area is therefore zero. This corresponds to zero for the total
displacement.
Graph
Positive to negative for y axis
Maximum height occurs at time t = u / g
Projectile
A projectile is any object acted upon only by the force of gravity
Projectile 1
The acceleration of the object is always equal to g and is always downwards because the force of gravity acts downwards.
The acceleration therefore only affects the vertical motion of the object.
Projectile 2
The horizontal velocity of the object is constant because the acceleration of the object does not have a horizontal component.
Projectile 3
The motions in the horizontal and vertical directions are independent of each other.
Vertical projectile
Such an object moves vertically as it has no horizontal motion. Its acceleration is 9.8 ms-2 downwards. Using the direction code + is
upwards, - is downwards, its displacement, y, and velocity, v, after time t are given by
V=u - gxt
y=uxt - 1/2 x gxp
Horizontal projected
A stone thrown from a chilf top follows a curved path downwards before it hits the water. If its initial projection is horizontal its path through the air becomes steeper and steeper as it drops
the faster it is projected, the further away it will fall into the sea
the time taken for it to fall into the sea does not depend on how
fast it is projected.
Suppose two balls are released at the same time above a level
floor such that one ball drops vertically and the other is projected
horizontally. Which one hits the floor first? In fact, they both hit the
floor simultaneously.
They are both pulled to the ground by the force of gravity, which
gives each ball a downward acceleration g. The ball that is projected horizontally experiences the same downward acceleration as the other
ball. This downward acceleration does not affect the horizontal motion
of the ball projected horizontally - only the vertical motion is affected,
The effects of air resistance
The effects of air resistance
A projectile moving through air experiences a force that drags on it
because of the resistance of the air it passes through. This drag force is
partly caused by friction between the layers of air near the projectile’s
surface where the air flows over the surface.
The drag force:
acts in the opposite direction to the direction of motion of the
projectile, and it increases as the projectile’s speed increases
has a horizontal component that reduces both the horizontal speed
of the projectile and its range
reduces the maximum height of the projectile if its initial direction is above the horizontal and makes its descent steeper than its ascent.
