The study of Kinematics involves describing, measuring, and analysing motion without considering the forces and masses involved.
Scalars and Vectors
Scalars are physical quantities that can be described as a magnitude, with a unit (for example, 60km/h)
Examples of Scalars include time, distance, volume, and speed
Scalars are represented by a simple italic symbol, such as t for time or d for distance
Vectors are physical quantities that can be described as a magnitude, a unit and a direction (for example, 20m West)
Examples of Vectors include position, displacement, velocity, acceleration, and force
Vectors are represented using VECTOR NOTATION.
The most common type of vector notation uses an arrow above the symbol, for example $\vec{v}$ for Velocity
Adding and Subtracting Vectors Using Algebra (One Dimension)
When adding or subtracting vectors using algebra, a sign convention must be established to represent the direction
For example, positive for forwards and negative for backwards
When using a sign convention it is CRUCIAL to provide a key explaining the convention used.
Using a sign convention allows you to enter the directions and magnitudes into your calculator. The sign of the final magnitude gives the direction of the total vector.
Steps for Adding
Apply the sign convention to change each of the directions to signs
Add their magnitudes and their signs together
Refer to the sign convention to determine to direction of thr resultant vector
State the resultant vector
Example:
A student walks 25m forward, then 16m backward, then 44m forward, then 12m backward. Determine the total displacement.
Forward is positive
25m forward = 25m
16m backward = -16m
44m forward = 44m
12m backward = -12m
$25-16+44-12 = +41$
Positive is forward
Therefore, the total displacement is 41m forward.
Steps for Subtracting
Apply the sign convention to change each of the directions to signs
Reverse the direction of the initial vector by reversing the sign
Do vector addition with the results
Example:
An aeroplane changes course from 255m/s West to 160m/s East. Determine the change in velocity.
West is negative
225m/s West = -255m/s $\vec{v}_1$
160m/s East = 160m/s $\vec{v}_2$
Reverse the initial vector: $-\vec{v}_1$ = 255m/s
Add the vectors: $-\vec{v}_1 + \vec{v}_2 = 225+160 = 415m/s$
Positive is east, therefore the change in velocity is 415m/s East
Displacement, Speed and Velocity
This section will explain the terms and concepts of RECTILINEAR (straight-line), such as position, distance, displacement, speed and velocity.
Center of Mass
An object’s motion is described in terms of their CENTER OF MASS, a single point which is the balance point of the object.
Position
Position describes the location of an object at a certain point in time with respect to the origin.
Position is a vector quantity and therefore requires a direction. The absolute reference frame for the direction is the origin of the object.
Position is measured in metres.
Distance Travelled
Distance Travelled describes how far a body travels during a journey.
Distance is a scalar quantity and is measured in meters.
Displacement
Displacement is the change in position of an object, and is represented by the symbol $\vec{s}$
Displacement considers only the starting point and ending point
In other words, the displacement of an object is the straight-line distance between its start and end points
Displacement is calculated by subtracting the initial position from the final position
Displacement is a VECTOR and therefore must have a direction as well as a magnitude
Displacement-Time Graphs
Displacement-time graphs can be used to summarise the motion of an object
The gradient of the graph at any point is the velocity at that point
Speed and Velocity
Speed is the rate at which distance is travelled
Speed is SCALAR
Velocity is the rate at which displacement changes
Velocity is a VECTOR
Speed and velocity are both measured in $m/s^2$
Instantaneous Speed and Velocity
How fast an object is moving at a particular point in time
The instantaneous speed is ALWAYS equal to the magnitude of the instantaneous velocity
Average Speed and Velocity
Indication of how fast an object is moving over a period of time
Average Speed: $v_{av} = \frac{\text{Distance Travelled}}{\text{Time Taken}} = \frac{d}{\Delta t}$
Average Velocity: $\vec{v_{av}} = \frac{\text{Displacement}}{\text{Time Taken}} = \frac{\vec{d}}{\Delta t}$
Converting between km/h and m/s
To convert km/h to m/s, divide by 3.6
To convert from m/s to km/h, multiply by 3.6
SUVAT Equations
These can also be expressed with different subjects:
