# Motion:

is one of the most basic and fundamental activities in the universe. Stars, planets, comets, satellites are all in motion. Planet earth rotates as well as revolves as p[art of its incessant motion within the solar system.

Motion is often described as 'relative.' This implies that in a given situation the same activity may appear as stationary to one observer while another observer might see it differently. For eg…..let's take the case of an aeroplane speeding along the runway….about to take off!! For two co-passengers sitting next to each other…..each one appears stationary with respect to the him/herself & to the plane. This is because both are moving together within the same plane at the same speed. However, both find themselves moving with respect to the airstrip/ground outside the plane with considerable speed. Likewise, an outside observer finds the people within the plane moving very fast.

**Concepts of distance & displacement: (9 April 2010)**

Distance is a scalar quantity while displacement is a vector quantity. A scalar quantity only has magnitude whereas a vector quantity has both magnitude and direction. If I say….a car travels a distance of 100km (magnitude)…I am referring to distance. If I say…a car travels 100km (magnitude) to the West (direction)…I am referring to displacement.

Concepts of distance and displacement when coupled with time give us the quantities of SPEED & VELOCITY.

**Uniform and Non-Uniform Motion: (13 April 2010)**

When a body covers/travels equal distance in equal intervals of time…we say it is performing uniform motion. The word 'uniform' implies similarity….sameness. A school 'uniform' ensures that all kids in the school have uniformity in their dress-up for a given day. In the same way, in physics uniform motion is typical of a body that displays sameness in its motion over a period of time.

Lets take up an example….I am sure you must have heard of Usain Bolt…the fastest man in the world. If not, then please wake up!!! He is the current 100m sprint World & Olympic Gold winner….and that too with extraordinary records!! When Bolt starts off the race from the blocks, his speed is zero at the very beginning. But over the next 100m he builds it up in such a way that at the finish line his speed is maximum. This is a typical example of non-uniform motion…..Usain covers unequal distances in equal intervals of time. For every 10m that he runs, he picks up his speed. Thus, for the stretch 20 to 30m the speed that he has is less than what he has for the 60 to 70m stretch.

A marathon runner who has to cover a long distance is much more likely to run in stretches where he maintains uniform motion. In these stretches his speed remains the same…and he covers equal distances in equal intervals of time.

From the above we can conclude….that uniform motion is non-accelerated motion, whereas non-uniform motion is accelerated motion. Why?? We shall discuss this a little later.

Nikhil

**15 April 2010**

Concept of **Average Speed** helps us to get an idea of how fast or slow we are traveling over a longish stretch of a road (say)……. I drove to my parents' house in Dehra Dun about a week ago. Starting very early….4am!!….I was able to cover good distance till about 7am. My parents house is about 245km from mine in Ghaziabad. In the first 3 hours….from 4am - 7am….I covered about 175km. I finally reached my destination at 9am. **Can you guys tell me what my average speed was??**

Average Speed = Total distance/Total time

As regards **Average Velocity**….which is a vector quantity…we generally use the concept of initial velocity (u) and final velocity (v).

Average Velocity = (u + v)/2

Velocity….being a vector…is dictated by both magnitude and direction. Suppose a car is moving at **45km/hr**(magnitude) **westwards** (direction). If either of the two……'45km/h' or 'westward' changes….we say that the velocity has changed. Thus, if we now have 45k/h moving southwards….we can say that velocity has changed….which implies that **acceleration** is coming into play!!

When velocity changes uniformly over a period of time…we call it **uniform acceleration**. Suppose….

- at t=0sec, u=5m/s…and for t=10sec, v=25m/s. Then rate of change of velocity = (v-u)/t = (25-5)10 = 20/10 = 2m/s
^{2}
- at t=10sec, u=25m/s…and for t=20sec, v=45m/s. Then rate of change of velocity = (45-25)/10 = 20/10 = 2m/s
^{2}

In both cases we find that the rate of change of velocity remains uniform, or conserved. This implies **uniform acceleration** or that the rate of change of velocity is not changing.

**Now coming to acceleration:**

Suppose u=initial velocity; v=final velocity; t=time taken for u to become v

Then, change of velocity = (v-u) in t seconds

Applying unitary method….we have:

In t seconds…….change in velocity = (v-u)

Therefore, in 1 sec……..change = (v-u)/t

**This per second change in velocity is referred to as acceleration. Its units:**

a = (v-u)/t……Now putting the SI units below:

= (m/s)/s

= m/s^{2}

**Thus, the SI unit for acceleration becomes m/s**^{2}

Acceleration a = (v-u)/t

If we multiply both sides by t we get:

at = v-u

**or v=u+at……….this is the First Equation of Motion. We have just derived it using basic definitions and the unitary method**

Nikhil

**16 April 2010**

We start with graphical representation of motion from next week. Please complete your notes by the weekend.

Nikhil