Speed:
Speed is the rate at which an object covers a distance. Speed is a scalar quantity. It has no direction .
Velocity:
Velocity may be defined as the rate of change of displacement.
Or
It can be also defined as : “ rate of change of position of an object.”
Velocity is a vector quantity. It has direction.
For example : If an object moving with a speed of 65 km / hr towards East direction. Then we say its speed is 65 km/hr East.
Dislacement Time Graph
Displacement-Time graph is important to interpret mathematical expression into picture as a graph. Graph gives a short cut idea about the concept of the mathematical statement. In Displacement time graph the slope of the curve is the velocity. If the curve is straight line then it means that the velocity is constant.
In a graph the straight line is called a curve despite it may be a straight line. Watch the video.
This video contains:
- displacement-time straight line curve and its meaning.
- Two curves have shown to physically interprete the race competition of two person.
- Initial displacement explained.
- When displacement-time curve takes the shape of a parabola.
Velocity Time Graph
Velocity-Time graph gives two most important parameter.
1) Its slope gives the acceleration.
2. The area under the curve gives the distance traveled by an object.
Here we will derive velocity(v = u + at) equation as shown the figure.
And
we will also derive graphically distance (s = ut + 1/2 a t2) equation. Analytically we can derive velocity equation as follow.
s = distance
v = final velocity
u = initial velocity
t = time
Acceleration = rate of change of velocity.
a = (v-u) /t
at = v – u
v = u + at Which is the equation of velocity.
Analytical derivation of distance equation.
distance = velocity x time
s = v.t
If the acceleration is uniform , then velocity will change its value uniformlly. i.e. v= 1/2 (v + u)
s = v.t
s = 1/2 (v + u). t
But v = u+ at
Putting the value of v in above equation we get
s = 1/2 {(u + at) + u}. t
s = 1/2 (2u + at). t
s = 1/2 .2u. t + 1/2. at 2
s = u t + 1/2 at 2 Which is the equation of distance in terms of u and t
Let us explain this graph. An object start moving with an initial velocity u . It moves with this constant velocity (u) for T second. After that it retards with acceleration a and stops after t second. After that it returns backward and accelerat for t second with an acceleration a. See the negative side graph of y-axis. It accelerates for t seconds. Then it moves with constant velocity u for further T seconds and come back to its original position. The distance covered is same in the forward and backward journey. Therefore area under the upper curve and lover curve is same.
How can We Specify the Position of an object | Physics Class 9
To specify the position of an object, we need a point with respect to which we identify the position of that object. This point is known as the origin or reference point.
Consider a man starts walking from point O. First he goes to point P and then to point Q. as we can see in the given image.
We can say that the position of the object is OP form the origin O in direction of x-axis and PQ from origin O in direction of y-axis. In term of co-ordinate system we say it as (OP, PQ) or (5,4) in term of actual value of axis.