Hello and welcome to physicscatalyst.com
This video is about the concept of velocity. So let us now begin by defining the term velocity
The concept of velocity is the rate of change of position of an object with the passage
of time in a given direction. We have only encountered similar definition when we are talking about speed because speed
is nothing but rate of change of position of an object with the passage of time
But there is a very important difference between speed and velocity and this difference is
nothing but direction. So when we are talking about speed we are only talking about the magnitude, but when
we are talking about velocity we are talking about both magnitude and direction
So in other words we can say that when we have information about both the speed and
direction of motion of moving object we have its velocity. For example if we say a train travels at 40 kilometers per hour then we know its speed
But if we say it is moving at 40 kilometers per hour towards the north then we know its velocity
So we can say that speed is a description of how fast and the velocity tells us about
how fast and in what direction
Mathematically velocity is given as displacement covered per unit time
Now as we discussed earlier velocity has both magnitude and direction
So velocity is a vector quantity
Now since velocity depends on displacement and we know that displacement can be positive
negative or zero. So velocity of a moving object can be positive, negative or zero
Now SI unit of velocity is meter per second and CVS unit of velocity is centimeter per
second and dimensional formula of velocity is N to the power zero L to the power one
T to the power minus one, there we know that N is the dimension of mass, L is the dimension
of length and T is the dimension of time
Let us now look at different types of velocity. So first type of velocity is uniform velocity
A body is said to be moving with a uniform velocity if it covers equal displacement in
equal intervals of time. No matter how small the time interval may be
Second type of velocity is variable velocity. A body is said to be moving with variable velocity if either its speed changes or direction
of motion changes or both speed and direction of motion changes with the change in time
Now third type of velocity is average velocity. Now we take average velocity of a moving object when the object is moving with a variable
velocity and this average velocity is defined as the ratio of its total displacement to
the total time interval in which the displacement occurs. So mathematically average velocity is equal to total displacement divided by total time
If x1 and x2 are the position of object at time t1 and t2 then average velocity from
time t1 to t2 is given by g average is equal to x2 minus x1 divided by t2 minus t1 which
is equal to delta s upon delta t. Now fourth type of velocity is instantaneous velocity
So the velocity of an object at a particular instant of time or at a particular point of
its path is called instantaneous velocity which is equal to the limiting value of the
average velocity of the object in a small time interval taken around that instant of time
So instantaneous velocity is given as g is equal to limit delta t tends to 0 delta x
divided by delta t which is equal to dx upon dt. This instantaneous velocity of an object is equal to first order derivative of its displacement
with respect to time. This is it for now. Thanks for watching