What is Speed?
Some bodies move fast and move slow.In order to have a comparison between fast and slow moving bodies we have to define a physical quantity known as speed.
Speed is the ratio of distance traveled to the time taken in travelling.
Average speed can easily be calculated by dividing distance covered by a moving body from time taken by the body to cover that specific distance.
Average speed = Distance / Time
S.I Unit of speed is m/s
What is Velocity?
Velocity is also the speed of a body but it is always have a specific direction.Speed refers only to time rate at which body is moving where as velocity refers to both speed and direction.
S.I Unit and formula of Velocity is same as of speed
What is the Difference between Speed and Velocity?
1 *Speed is a scalar quantity meaning it only requires a number to define is effect.
*Velocity is vector quantity meaning it requires a number and also a direction for its proper definition.
2 *Formula of speed is written as V= Distance / Time
*Formula of velocity is written as V(arrow over V) = Distance / Time
What is Acceleration?
When Velocity of a body changes acceleration is produced.This change of velocity can be produced either by changing direction or speed or may be both of them,.
In other words acceleration is the rate of change of velocity of a body.
In mathematics change in velocity can be written as
change in velocity ΔV=Vi-Vf
And change is velocity in unit time is = ΔV / Δt
So Acceleration can be written as (arrow above a) a = ΔV / Δt
S.I unit of Acceleration is m/s2
Equations of motion
Three equations of motion are derived in the following
First equation of motion
Suppose a body is moving with a velocity V1 and it is accelerated for time T in a way that its final velocity after acceleration becomes V2.
mathematically it can be written as
Change in velocity of body in time T = V2 - V1
Therefore change in velocity in unit time = (V2 - V1) / T
As we know that change in velocity in unit time is Accleration
So Acceleration a = (V2 - V1) / T
or it can also be written as at = V2 - V1
or at + V1 = V2
This is called First equation of motion.And it says that final velocity of a body is the sum of initial velocity to product of acceleration and time.
Second equation of motion
Suppose a body starts with an initial velocity V1 and travels with a uniform acceleration "a" for a time "t". Let the distance covered by this body is "S" and final velocity V2
Since acceleration is uniform so velocity changes at a constant rate.
Mathematically,
Average velocity = (V1+V2) / 2
Distance travelled = Average Velocity × time
Therefore S = ((V1+V2) / 2) × t)
From first equation of motion we have
V2 = V1 + at
putting the value of V2
So S = ((V1+(V1 + at)) /2 ) × t
S = (2V1.t + at^2) / 2
or S = V1.t + (at^2) / 2
Above equation is known as Second equation of motion and it gives a Relation of distance with acceleration , time and velocity.
Third Equation Of Motion.
Third equation of motion is the combination of first two equations and time is eliminated from the equation so it is basically a relation of Velocity to acceleration and distance.
From Eq 1
V2 = V1 + at
Taking square on both sides
(V2)^2 = (V1 + at)^2
Or V2^2 = V1^2 + 2V1.at + a^2.t^2
V2^2 = V1^2 + 2a(V1.t + 1/2 a.t^2)
From Eq 2 we have
V1.t + 1/2.a.t^2 = S
V2^2 = V1^2 + 2aS
This is the Third equation of motion.
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