O LEVEL PHYSICS - KINEMATICS

Kinematics is a branch of Mechanics that is concerned with pure motion and is not concerned with the forces involving those motion. 

Distance (in terms of kinematics) is length covered by a moving object.
Displacement is the linear distance between two points.
Displacement is the linear distance traveled by an object from the starting point to the endpoint.
Linear distance means distance in a straight line.
The  SI units of both Distance and Displacement is in meters(m).
Distance is a scalar quantity.
Displacement is a vector quantity.

Let's look at this concept with an example.

Example 1:

Suppose a car travels from A to B and then from B to C (see diagram). What is the car's total distance and displacement?  

Answer: The car's total distance is the length that it moved. That is,
distance = 15 + 7 = 22m

And it's displacement is

displacement = 10m

Because this is the linear distance covered between the starting and the endpoint.



The car now further travels from C to A. What is now the car's total distance and displacement starting from A and traveling back to A?

Answer: Now the total distance will be,
distance = 22 + 20 = 40m

And the total displacement will be
displacement = 0m

Because the starting and endpoints are the same and there is zero meters of linear distance in between them.  






Now moving on to speed and velocity.

Speed is rate of change of distance. It is measured in meters per second (m/s). It is a scalar quantity.

speed = distance traveled / time taken

Velocity is the rate of change of displacement. It is also measured in meters per second (m/s). It is a vector quantity.

velocity = displacement / time taken  




You would find plenty of examples on speed/velocity calculations on your book. Therefore I am not adding another one here. Next we are going to look at Acceleration.

In the simplest of terms...


Acceleration is the rate of change of velocity. It is measured in meters per second square (m/s^2). 
It is vector quantity.   

acceleration = change in velocity / time taken
 
But the question still remains of what acceleration actually is or what is happens during acceleration.
So if we now look at a deeper definition...

Whenever there is a change in velocity, there is an acceleration. If the velocity is not changing then there is zero or no acceleration. But another thing to note is that velocity is a vector quantity so if the direction of an object changes, then it's velocity changes. Hence it's acceleration changes.
So, either change in magnitude or change in direction, both results in an acceleration. (This is an important point to note as this often comes as a conceptual question in CIE O Level Exams). 

There are two types of acceleration:

•  uniform acceleration
•  non-uniform acceleration  

Uniform acceleration
Uniform acceleration is when the rate of change of velocity remains constant.
Another name for uniform acceleration is constant acceleration. Constant acceleration means that the acceleration does not change but remains constant. It does not increase or decrease with time. 


But what actually does that mean?

It means that for an object traveling with acceleration of 5m/s/s every one second, it's velocity increases 5m/s each second. This means every one second, the object's speed changes like this 5m/s,  10m/s, 15m/s and so on. Thus the velocity changes by 5m/s each second (or each unit time).

It forms a straight line on a velocity-time graph.

Thus a formal definition would be...
Uniform acceleration is when the velocity changes at a steady rate.
 

Non-uniform acceleration
As you can assume from the definition above
Non-uniform acceleration is when the velocity does not change at steady rate.

For example, an object's velocity changes like this each second: 2m/s, 3m/s, 5m/s, 10m/s, 19m/s and so on. Thus I can no longer say that the velocity changes by the fixed, same unit every second. (In the example of uniform acceleration, it was changing by 5m/s each second). 

Remember,
Uniform means NOT CHANGING, non-uniform means CHANGING.

  
Note that these do not hold the same meaning as acceleration and deceleration.

Acceleration is also known as positive acceleration. When an object speeds up it is called positive acceleration.
When an object speeds up with time it is called positive acceleration.
An upward sloping graph represents positive acceleration in a velocity time graph.

Your syllabus describes deceleration as negative acceleration. When an object slows down it is called deceleration or negative acceleration.
When an object slows down with time it is called deceleration.
A negative slope represents deceleration in a velocity time graph. 

Note that this just a simple representation of the concept using straight lines. These could be curves as well. What is important to notice over here is the slope of the graph which shows acceleration and deceleration.






Distance-time Graphs
Gradient = y-axis/x-axis

The gradient of a distance-time graph is speed.
The gradient of a velocity-time graph is acceleration.

The unit of the speed/velocity shown on the gradient can be found from the x and y axes of the gradient. Generally it is either m/s or km/h.

Note that since distance is a scalar quantity, a distance-time graph only goes in one direction. But change of direction can be shown in displacement-time graph. 

If you have any other queries about speed time graphs, just write it in the comments section below.








 
Velocity-time Graphs
The gradient of a velocity-time graph is Acceleration.

The area under a velocity-time graph gives the distance traveled. 

    We know that the steeper a graph, the greater the gradient. Thus a steeper v-t graph means higher acceleration. 
We also know that the area under a v-t graph gives the distance traveled. Review these things when you study.







Free-fall acceleration  
The acceleration caused by the pull of Earth's gravity is constant near the Earth's surface and is approximately 10m/s/s. This is called acceleration of free fall and is denoted by g.

g=10m/s/s
(We now know what constant/uniform acceleration means.)






Motion of bodies with constant weight falling with and without air resistance 
(This section requires knowledge from the chapter Newtonian Mechanics).

Because there are plenty of diagram based explanations and graphs of these in books, I am going to keep it brief and to the point only.

Falling without air resistance   
Any object falling near the earth's surface experiences a force called air resistance that tends to slow the object down.

To observe the effect of falling body without air resistance, we carry it out in a vacuum container. In a vacuum container, air resistance does not act on a falling object.

When the object falls, the only force acting on the object is gravity. Thus the object accelerates until it hits the ground. This is called free-fall acceleration.
Because the earth's pull on every object is the same, objects hit the ground at the same time in a vacuum tube. For example, a feather and a coin will hit the ground with the same speed and at the same time. (They both accelerate at 10m/s/s).

Falling with air resistance  
An object falling near the earth's surface experiences a force called air resistance. Air resistance is force that acts in the opposite directing of a falling object (it acts upwards) and tries to slow the object down. Air resistance increases as the speed of the falling object increases.

So the object initially falls with uniform, free-fall acceleration that is 10m/s/s. As the object falls, it's speed increases and hence, air resistance increases. This happens until the the air resistance is equal to the weight of the falling object. The object then starts to travel with a uniform velocity called terminal velocity until it hits the ground.





This is quite a big chapter guys. Stay calm and study. Best wishes!

-Your tutor.