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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:

[pic]

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:

[pic]

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:

[pic]

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:

[pic]

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.

[pic]

The shaded area in this case also gives the distance moved by the object:

[pic]

Graph for non uniform acceleration:

[pic]

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:

[pic]

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

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