Motion Flashcards
Scalar Quantity
A quantity with magnitude (size) but no direction
Scalars can be added and subtracted normally
They can be multiplied and divided
Scalar Quantities Examples
Quantity: SI unit
length: m
mass: kg
time: s
speed: ms^-1
temperature: K, °C
volume: m^3
energy: J
potential difference: V
power: W
Vector Quantity
A quantity with magnitude (size) and direction
Represented by an arrow:
The length is it’s magnitude
Arrow head shows it’s direction
Not all vectors are to scale, but will be labelled with their measurement
Vector Quantities Examples
Quantity: SI unit
displacement: m
velocity: ms^-1
acceleration: ms^-2
force : N[kgms^-2]
momentum: kgms^-1
Distance and diplacement
Measured in metres
Distance is a scalar quantity
Displacement is a vector quantity (with direction)
The angle from the vertical is also shown
Adding Vectors / Parallel Vectors
Magnitude and direction must be taken into account
Value found is the resultant vector
If the vectors are parallel (acting in the same line and direction) -> Just add them together to find the resultant vector
Vectors in opposite directions
Antiparallel vectors (acting in the same line but in opposite direction)
One direction (usually to the right) is considered positive and the opposite direction is considered negative
The vectors are added to find the resultant
Two perpendicular vectors
Vectors acting at right angles to each other
The vectors are drawn tip to tail
As they are perpendicular, we can use Pythagoras and trig to find the magnitude and direction of this vector
You can also calculate the angle ϴ with the horizontal or vertical vector
Resolving Vectors
Taking a resultant vector and splitting it into two perpendicular components
Done for ant vector at an angle e.g. Force, Velocity, Displacement, Momentum
Distance and Speed
The average speed v, of an object can be calculated from the distance travelled x, and the time take t, using the equation
Average Speed = distance travelled / time take
v = Δx / Δt
v: velocity in ms^-1
Δ: (delta) change in
Distance-Time graphs - Scalar
Used to represent the motion of objects
Distance on the Y-axis
Time on the X-axis
The gradient of a graph gives the speed of the object
Instantaneous Speed
The speed of the car over a very short interval of time
Calculated by drawing the tangent to the distance-time graph at that time, then finding the gradient of this tangent
Can be calculated when speed in varying (Not a straight line)
Displacement and Velocity
Displacement s, is a vector quantity unlike distance (scalar)
Velocity is a vector which is calculated from displacement
Average velocity = change in displacement / time taken
v = Δs / Δt
Units for velocity is ms^-1
Displacement-Time graphs - vector
Displacement on the Y-axis
Time on the X-axis
The gradient of a graph gives the velocity of the object
If the graph is not a straight line, then draw a tangent to the graph, find the gradient of the tangent -> Instantaneous velocity
Acceleration
The rate of change of velocity
a = Δv / Δt = s / t^2
a = (v - u) / t [SUVAT equation]
The units are ms^-2
Vector quantity: Magnitude and Direction
Acceleration for a velocity-time graph
The gradient of a velocity-time graph is the acceleration
a = Δv / Δt = Δy / Δx = m
Calculating displacement for changing accelerations
Count the squares under the graph - The area under the graph is displacement
Use b x h to find the area of one square
Then count the squares that are almost full in a graph
Then calculate how many remaining bits of squares to the nearest integer
Multiply the total number of squares by the displacement that one square represents
Equation for Uniformly Accelerated Motion
SUVAT
Acceleration is constant (Air resistance is ignored)
v = u + at
s = 0.5(u + v)t
s = ut + 0.5at^2
v^2 = u^2 + 2as
s = ut - 0.5vt^2
s: displacement / m
u: initial velocity / ms^-1
v: final velocity / ms^-1
a: acceleration / ms^-2
t: time / s
Derivation of v = u + at
Gradient of graph is acceleration
a = Δx / Δy = (v - u) / t -> at + u = v
Derivation of s = 0.5(u + v)t
Average speed is distance over time
(u + v) / 2 = s / t or s = 0.5(u + v)t
Derivation of s = ut + 0.5at^2
Area under graph is displacement
s = ut + 0.5t(v-u)
a = (v - u) / t ->
s = ut + 0.5(v - u)t^2 / t
s = ut + 0.5at^2
Derivation of v^2 = u^2 + 2as
s = 0.5(u + v)t -> t = 2s / (u + v)
v = u + at
Substitute to get v^2 = u^2 + 2as
Car Stopping Distances
The total distance travelled from when the driver first sees reason to stop, to when the vehicle stops
Split into Thinking distance and Braking distance
Stopping distance = Thinking distance + Braking Distance
Thinking Distance
The distance travelled between the moment when you first see reason to stop, to the moment when you use the brake
