Chapter 08––>Motion

Introduction

We say that an object is in motion when its position changes with time.

To describe the position of an object we need to specify a reference point called the origin.

Motion along a Straight Line

Distance: Total ground covered by an object during its motion between any two points.

Displacement: The shortest distance measured from the initial to the final position of an object.

Distance is a scalar quantity (it only has magnitude no direction) whereas Displacement is a vector quantity (it has both magnitude and direction)

When we draw a straight line with the help of a ruler the tip of pencil move in a straight line.

Uniform and Non-uniform motion

As the object covers equal distances in equal intervals of time, it is said to be in uniform motion.

Note: The time interval in this motion should be small.

Example- Motion of planets around Sun, they revolve at a constant speed. So the distance travelled in every equal time period is equal

Motions where objects cover unequal distances in equal intervals of time are considered non-uniform.

Example- Atheltes running, they are slow initally in their race but as the race preogresses their speed increases. Let us say they cover 1 km in the first hour , and after 1 hour they cover 3 km, so the distance covered in 1 hour is changing .

Note: If rate of change of any quantity with time is constant, it is said to be Uniform.

Speed and Velocity

—————————————–

Speed: Distance travelled by the object in unit time.
The SI unit of speed is metre per second. This is represented by the symbol m s^–1 or m/s.
Speed is a scalar quantity; it only has direction.

Velocity: Velocity is the speed of an object moving in a definite direction.
The SI unit of velocity is also metre per second.
Velocity is a vector quantity; it has both magnitude and direction.

In most cases, objects will be in non-uniform motion. Therefore, we describe the rate of motion of such objects in terms of ‘average’.

Example: Consider yourself going to a shop on a cycle, you stop cycle many times on the way and then you come from the shop to your home. Distance from shop to home = 3 km, time taken from home to shop = 1 hour and time taken from shop to home = 2 hour.

Average speed = total distance / total time

= (3+3) / (1+2) = 2 km/hr

Average velocity = displacement / total time

= (3-3) / (1+2) = 0 km/hr

Acceleration

Acceleration: It is a measure of the change in the velocity of an object per unit time.
Acceleration can be caused either by change in direction of motion or change in speed or both.

SI unit is ms^-2.

It is a vector quantity; the acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the direction of velocity.

When you apply brakes on a car the velocity is in forward direction but acceleration is in backward direction, so acceleration will be negative. It is also called deceleration.

When you are increasing the speed of a car the acceleration is positive as velocity and acceleration are in both in the forward direction

(The acceleration in this jet pack is provided by thrust)

Graphical representation of Motion

Distance-Time Graph

In this graph, distance is taken along the y-axis and time is taken along the x–axis.

For uniform speed, a graph of distance travelled against time is a straight line, as rate of change of change of distance with respect to time is constant

Velocity-Time Graph

In this graph, velocity is taken along the y-axis and time is taken along the x–axis.
For uniform acceleration, a graph of velocity against time is a straight line.

The area enclosed by velocity-time graph and the time axis will be equal to the magnitude of the displacement.

Equations of motion by graphical method

Equations of Motion by Graphical Method

Velocity-Time Relation

A car having initial velocity u , is being subjected to a uniform acceleration a for a time period of t , after the time t the final velocity of the car is v.
Now we need to find the relation between v,u,a,t graphically.

Position-Time Relation

A car having initial velocity u , is being subjected to a uniform acceleration a for a time period of t , after the time t the final velocity of the car is v.
In the time interval of time t , it covers a distance of s.
Now we need to derive relation between s,u,a,t graphically.

Position–Velocity Relation

A car having initial velocity u , is being subjected to a uniform acceleration a for a time period of t , after the time t the final velocity of the car is v.
In the time interval of time t , it covers a distance of s.
Now we need to find relation between s,u,v,a graphically.

Uniform Circular Motion

In circular motion the direction of speed i.e. velocity, changes at every moment.

When an object moves in a circular path with uniform speed, its motion is called uniform circular motion.

In uniform circular motion speed of object remains constant, but its velocity changes at every moment, thus providing acceleration.