Motion

                                                  

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

For example ,Let us assume that a hospital in a village is 2 km north of the railway station.  We 

have specified the position of hospital with respect to the railway station. In this example , the railway station is  the reference point(origin). We could have also chosen other reference points according to our convenience.

Difference Between Distance and Displacement.

Distance : Suppose a car start its journey from O which is treated as its reference point(origin).         

                                                       Fig 1

From O  it goes to B and back to C.

Total Distance cover by car =OB+BC

=35+10=45KM

So What is Displacement.

Displacement = OC

=25KM

Displacement is the shortest distance measured from the initial position (O) to the final position(C).      

The numerical value of a physical quantity is its magnitude.

Can the magnitude of the displacement be equal to the distance travelled by an object?

Consider the example given in fig 1. If car move from O to C. Then distance cover is 25KM and

Displacement is also 25KM.Durning it motion from O to B and B to C,

The distance cover is OB+BC=35+10=45KM.While displacement is 25KM.

Thus displacement is not equal to path length in this case.

Further ,we will notice that the magnitude of the displacement for a couse of motion may be zero

But the corresponding distance covered is not zero. If our car move from O to A and come back to O.

Than distance travelled is OA+AO=60+60=120KM.But displacement is 0 because distance between final and initial position is 0.

Uniform Motion And Non Uniform Motion

Uniform Motion:-  When an object cover equal distance in equal interval of time .it called to have uniform motion. For example , if a car cover 40KM in1st Hours ,40KM in 2^nd hour and so on .It said to have uniform motion.

Non uniform Motion:-  If the car travelled 40KM in 1^st  Hours ,60 Km in 2^nd  Hours ,70KM in 3^rd Hour so on. Then it said to have non uniform motion.

Speed:- 

It is distance travelled by an object in unit time. To specify the speed of an object, we require only its magnitude. The speed of an object need not be constant. In most cases ,objects will be in non uniform motion. Therefore , we describe the rate of motion of such object in term of their average speed. The average speed of an object is obtained by dividing the total distance travelled by the total time taken. That is,

Average speed  v =d/t

Where  d= Total distance Travelled

t = Total time taken

The SI unit of speed is metre per second. This is represented by the symbol  ms-1 or m/s.

The other units of speed include centimetre per second(cm/s) and kilometre per hour(km/h).

Velocity

Velocity is the speed of an object moving in a definite direction. The velocity of an object can be uniform or variable.it can be changed by changing the object’s speed, direction of motion or both.

When an object is moving along a straight line at a variable speed, we can express the magnitude of its rate of motion in term of average velocity.It is calculated in the same way as we calculate average speed.

In case the velocity of the object is changing at a uniform rate ,then average velocity is given by the arithmetic mean of initial velocity and final velocity for a given period of time.

Where v= average velocity

             U= initial velocity,

              f= final velocity

Also

ACCELERATION :-RATE OF CHANGE OF VELOCITY

Aceelaration is a measure of the change in the velocity of an object per unit time. That is

               

Acceleration =  

                         

If the velocity of an object changes from an initial value u to the value v in time t,

The acceleration a is

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. The SI unit of acceleration is ms^-2.

  If an object travel in a straight line and its velocity increases or decreases by equal amounts in equal internals of time ,then the acceleration of the object is said to be uniform. the  motion of a freely falling body is an example of uniformly accelerated motion. On the other hand, an object can travel with non-uniform acceleration if its velocity changes  at a  non-uniform rate. For example, if a car travelling along a straight road increases its speed by unequal amounts in equal interval of time,then the car is said to be moving with non-uniform acceleration.