KINEMATICS!
Introduction:
Welcome
back! Hope you all are good. Today we are going to learn an important topic,
that is kinematics. The big question: what is kinematics? It is the study of
speed, velocity, time and acceleration. We’ll study these quantities in more
detail in this tutorial.
Definition:
Okay
so starting with speed and velocity, speed is defined as the distance
travelled by an object in a given time, or more simply as distance travelled
per unit time. While on the other hand velocity is displacement per unit
time. So then, what is the difference between the two? The difference is the
same as that between distance and displacement; Speed is a scalar
quantity while velocity is a vector. Now, what is scalar and what is
vector? Well, scalar quantities are those which have a magnitude only, while
vector quantities have both a direction and a magnitude. Just to further clear
it out, consider a car going at a speed of 40 m/s. We are not told whether the
car is going northwards, down the hill or whatever. So what is 40m/s? It’s
speed. A bit easier now?
How to calculate average speed?
Average
speed can be calculated using the formula:
Average Speed = Total Distance Travelled /
Total Time Taken
Q1. The distance b/w town A and town B is 25
km . A car travels from town A to town B and then returns to town A . The total
time taken is 5 hours. What was the average speed of the journey?
Uniform acceleration:
Acceleration
is the rate of change of velocity. Simple as that!
Acceleration = (Final Velocity - Initial
Velocity) / Time
Q2. A
car starts from rest and travels in a straight path. It reaches a speed of 40
m/s in 8 seconds. What is it’s acceleration, assuming that it accelerates
uniformly?
If
we know that the acceleration of an object is constant, we can find its average
velocity by a different formula, which is as follows:
Average Velocity = (Final Velocity +
Initial Velocity) / 2
Also
if an object is travelling with constant acceleration, then these equations of
motions are applicable.
●
2as
= v2 - u2
●
s =
ut + 1/2 at2
●
v =
u + at
●
2s
= (v + u)t
Key:
a =
acceleration , s = displacement, v = final velocity, u = initial velocity, t =
time
These
equations are very helpful in finding the unknown.
Non-uniform acceleration:
This
form of acceleration changes with time. In such case, the equations of motions
cannot be used.
Graphs:
Every
situation that can be considered can be represented graphically. It helps us in
various calculations and is easy to interpret. In such graphs, time is always
taken on the x-axis while distance on the y-axis.
Distance-Time Graphs:
Okay
so here are the distance-time graphs of three objects in motion. As we know the
gradient of distance-time graph represents speed. Object A is moving with
increasing speed a it’s gradient is increasing. Object B is moving with uniform
speed as it’s gradient is uniform. And similarly, as the gradient of C is
decreasing, it’s moving with a decreasing speed. Nothing too scientific, right?
Okay
so moving on to the graph of a stationary object, it should be covering any
distance, right? So that explains it all! The graph of a stationary will look
like this:
As
we can see, the object is stuck on the same distance. Let’s say 40 m, and it’s
on 40 m throughout. So it’s stationary, not moving, at rest!
Speed-Time Graphs:
So
here’s a speed-time graph for an object at rest:
Since
the slope is equal to zero, there is no acceleration. And secondly, the
velocity is zero, so object is at rest.
And
a speed time graph for an object moving at constant velocity:
Since
the slope is zero, the acceleration is obviously zero, right? And as there is
no acceleration, that is, change in velocity, the velocity is therefore
constant. Get it?
Okay,
and here’s a new concept: the area under a speed time graph gives the distance
moved by the object.
The shaded area in this case also gives the
distance moved by the object:
Graph
for non uniform acceleration:
Okay
so as we can that the slope of the graph is increasing, and we know that the
slope in a velocity time graph represents acceleration. Therefore, the
acceleration in this case is increasing. Easy, no? And again, the shaded area
in this case represents the distance travelled by the object.
So
to sum up:
●
The
gradient of a distance-time graph represents speed
●
The
gradient of a speed-time graph represents acceleration
●
The
area under a speed-time graph represents distance
Motion under free-fall:
The
acceleration due to the gravitational pull of the earth is always constant and
its value is 9.81 m/s2 . However, when a body falls from the sky, it
doesn't fall with constant acceleration. This is due to the resistance provided
by air which is present. As soon as the body accelerates the air resistance
acting on the body also increases. Very soon, the air resistance reaches the
point where it balances the weight of the body which means that the
acceleration of the body becomes zero, as the resultant force acting on it is
also zero (we will deal with forces in the next section). This causes the body
to fall with a uniform velocity; This velocity is known as terminal velocity. A
typical graph for motion under free-fall would look like this:
Task: Okay so finally, your assignment is
to google questions of kinematics and assess yourself to see if you have
grabbed the basic concepts.
Answers:
Q1: 10 m/s
Q2: 5m/s2
