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The relationship among different parameter like displacement velocity, acceleration can be derived using the concept of average acceleration and concept of average acceleration and instantaneous acceleration.
When acceleration is constant, a distinction between average acceleration and instantaneous acceleration loses its meaning, so we can write
where is the velocity at t = 0 and is the velocity at some time t.
So,
.................. (2)
This is the first useful equation of motion.
Similarly for displacement
.................. (3)
in which is the position of the particle at t0 and is the average velocity between t0 and later time t. If at t0 and t the velocity of particle is
This is the second important equation of motion.
Now from equation (2), square both side of this equation we get
This is another important equation of motion.
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