Today we’ll be covering:
 distance, displacement, speed, velocity, acceleration
 graphs of motion
 determine displacement from the area under a velocitytime graph
 determine velocity using the gradient of a displacementtime graph
 determine acceleration using the gradient of a velocitytime graph
 equations of motion
 uniformly accelerated motion in a straight line
Let’s get to it!
Some Basic Definitions
 Distance: total path length covered (where direction does not matter)
 Displacement: linear path length measured from initial position to finishing position
 Speed: rate of change of distance
 Velocity: rate of change of displacement
 Acceleration: rate of change of velocity
When dealing with changing velocities & accelerations, it is important to distinguish between:
AVERAGE velocity/ acceleration 
change in displacement/velocity over total time 
INSTANTANEOUS velocity/ acceleration 
change in displacement/velocity over a SMALL interval in time (expressed on a graph as the gradient of a TANGENT) 
Graphs of Motion
The motion of an object can be expressed as graphs of different values against time.
Behaviour of object 
DisplacementTime  VelocityTime  AccelerationTime 
Stationary at Origin 

Stationary in front of the origin 

Stationary behind the origin 

Constant Velocity 

Constant Velocity 

Constant Acceleration  
Constant Deceleration 

NonUniform Acceleration 
Finding the gradient & area below these graphs can also show the relationships between the aspects of motion:
Calculation 
DisplacementTime  VelocityTime 
AccelerationTime 
Gradient 
Velocity  Acceleration  – 
Area beneath graph 
– 
Displacement 
Velocity 
Uniformly Accelerated Motion
After understanding these basics, it’s useful to know the derivations of a group of equations that can be a handy shortcut when dealing with kinematics problems.
However, remember that they work only for UNIFORMLY accelerated motion.
The following equations are only applicable in a situation where..
 the acceleration of the object is CONSTANT
 the object is travelling LINEARLY (in 1 dimension)
There are other types of motion wherein these equations do NOT apply:
 Circular Motion
 Simple Harmonic Motion (Oscillations)
Since in these cases the object moves in 2 dimensions.
Kinematic Equations
Due to them containing the variables s, u, v, a & t,
these equations are commonly called the “SUVAT Formulas” by laypeople.
The equations are:
v = u + at
s = ½ (u + v)t
s = ut + ½ at^{2}
s = vt – ½ at^{2}
v^{2} = u^{2} + 2as
Derivations:
Let’s start with a basic equation for acceleration, which is change in velocity over time. a = (v – u)/tThis can be rearranged to v = u + at 
Next, think about the definition of AVERAGE VELOCITY:
Total distance over total time It is also known that average velocity is the sum of the initial & final velocity, divided by 2: Thus,

Next, the 1^{st} equation can be substituted into this one to get
s = ½ (u + u + at)t s = ut + ½ at^{2}

From v = u + at, you can rearrange to get
u = v – at s = (v – at)t + ½ at^{2} s = vt – at^{2} + ½ at^{2} s = vt – ½ at^{2}

From v = u + at, you can rearrange to get t = (v – u)/aSubstituting this into s = ut + ½ at^{2}s = u(v – u)/a + ½ a[(v – u)/a]^{2}s = (uv – u^{2})/a + (v – u)^{2}/2a2as = 2uv – 2u^{2} + (v – u)^{2}2as = 2uv – 2u^{2} + v^{2} – 2uv + u^{2} 2as = u^{2} + v^{2} v^{2} = u^{2} + 2as

Before solving a question, ALWAYS:
 Identify what you HAVE
 Identify what you NEED
 Identify the appropriate EQUATION to use
Free Fall Acceleration
On Earth, all objects are subject to a Gravitational Force.
This force accelerates all objects by 9.81 m s^{2} downwards (towards the Earth).
This value of acceleration is known as the constant, g.
This acceleration must be taken into account when dealing with the motion of falling objects.
In Free Fall, g is the ONLY VERTICAL force acting upon the object.
This means that the only source of acceleration is the Earth’s gravity, not any thrusters or jets on the object.
Air Resistance
For many problems, air resistance is NEGLIGIBLE.
You won’t have to worry about taking this into account.
However, once you cover Air Resistance in the next chapter,
there will be problems where you have to take it into account.
You can read up on Air Resistance here.
⇐ Previous in Physics: Measurements & Uncertainties
⇒ Next in Physics: Projectile Motion