Chapter 7 - Kinematics Flashcards
Displacement defintion
Distance in a given direction
Speed definition
Change of distance per unit time
Velocity definition
Change of displacement per unit time
- Speed in a given direction
- Rate of change of displacement
Speed equation
Speed = distance travelled/time
- v = s/t
Equation for constant speed in a circular motion
Constant speed on a circle of radius, r = 2πr/T
- T = time taken to complete one rotation
Shape of a distance-time graph for an object moving at constant speed
- Straight line with a constant gradient
- Speed = distance/time = gradient of the line
Motion of an object moving with constant velocity
- Moves at the same speed without changing its direction of motion
Acceleration definiton
Change of velocity per unit time
- Rate of change of velocity
What is the gradient of a velocity-time graph equal to?
The acceleration
What are the conditions of motion under which the kinematic equations apply?
- Uniform acceleration
- Motion along a straight line
Equstion for motion without displacement (s)
v = u + at
- derived from y = mx + c → velocity time graph
- y-axis = v, x-axis = t
- y-intercept = c = u
- gradient = x = t
What is non-uniform acceleration?
When the direction of motion of an object changes, or its speed changes, at a varying rate
How is non-uniform acceleration seen on a velocity-time graph?
- Curve
- Gradient represents acceleration so increases/decreases with time
- Second derivative is rate of change of acceleration
Equation for motion without acceleration (a)
s = ((u+v)t)/2
- derived from the area of a trapezium = 1/2(a+b)h → s = area under graph
- Can also be derived from average velocity = (u+v)/2 combined with s = vt
Equation for motion without time (t)
v^2 = u^2 + 2as
- Derived by combining a = (v-u)/t and s = ((u+v)t)/2
Equation for motion without final velocity (v)
s = ut + 1/2at^2
- Derived by combining s = ((u+v)t)/2 and v = u + at
How is displacement represented on a velocity-time graph?
From the area under the graph
Why does a heavy object not fall faster than a lighter one in a vacuum?
W = mg
- Acceleration due to gravity is constant
- g = W/m → When mass increases, weight also increases proportionally, so the increase cancels out in the equation for acceleration
How does the steepness of a slope affect acceleration?
- Acceleration is greater the steeper the slope
How to investigate the free fall of a ball?
- Take a multiflash photo or video of the ball’s flight as it falls after being released from rest
- Verticle metre rule provides scale
- Ordinary camera with slow shutter speed used to record ball’s descent in a dark room illuminated by a stroboscope flashing at a constant rate of about 20 flashes per second
- Record the distance fallen at a given time
- Calculate acceleration from s = ut + 1/2at^2
- Graph of s against t^2 will be a straight line through the origin with acceleration of 2 x gradient
When is an object in free fall?
When there are no external forces acting on the object apart from the force of gravity
What is the acceleration of free fall?
Acceleration due to gravity
- 9.81 ms^-2 when near the Earth’s surface
Motion of a ball thrown directly upwards on a displacement-time graph
- Immediately after being thrown, the velocity is positive and large so the gradient is positive and large
- As the ball rises, velocity decreases so gradient decreases
- At max height, velocity is zero so gradient is zero
- As the ball descends, its velocity becomes increasingly negative, so gradient becomes increasingly negative, as its now moving in the opposite direction
What is a projectile?
Any object acted upon only by the force of gravity
Key prinicples that apply to all projectiles
- Acceleration only affects the vertical motion of the object - acceleration always equal to g and acts downwards as force of gravity acts downwards.
- Horizontal velocity is constant because the acceleration does not have a horizontal component
- Motions in the horizontal and vertical directions are independent of each other
When do two objects reach the ground, one dropped vertically and the other projected horizontally, relative to each other and why?
- Both reach the ground at the same time
- Both experience the same vertical acceleration and start from the same vertical velocity (zero)
- Horizontal velocity independent from (has no effect on) vertical velocity
Why does an object projected velocity fall with a parabolic trajectory in the absence of air resistance?
- Horizontal velocity is constant - no horizontal velocity
- Vertical velocity increases at a constant rate - uniform vertical acceleration - vertical path gets steeper as it falls
When will an object experience projectile-like motion?
When the object has constant acceleration in a different direction to its velocity
What causes the drag force on a moving object?
- Air resistance - friction between the layers of air near the projectile’s surface where the air flows over the surface
How does the drag force act?
- Acts in the opposite direction to the direction of motion of the projectile
- Drag force increases as projectile’s speed increases
How does the drag force affect the horizontal motion of a projectile?
Horizontal component of drag force reduces the horizontal speed of the projectile and its range
How does the drag force affect the vertical motion of a projectile?
- Reduces its maximum height of the projectile if its initial direction is above the horizontal
- Makes its descent steeper than its ascent
How can the shape of the object cause a lift force?
When the shape casuses air to flow faster over the top of the object than underneath it
- Causes the pressure on the top of the surface to be less than on the bottom
- Pressure difference causes the lift force
Equation for vertical displacement when air resistance is present
y = UtsinΘ - 1/2gt^2
- Vertical displacement = UtsinΘ without air resitance
- Displacement 1/2gt^2 lower due to drag
Equation for vertical component of velocity when air resistance is present
V(y) = UsinΘ - gt
- Vertical velocity = UsinΘ without air resistance
- Velocity gt lower due to drag
