Instantaneous velocity is the velocity of an object in motion at a specific point in time. This is determined similarly to average velocity, but we narrow the period of time so that it approaches zero.
The formula for instantaneous velocity is the limit as t approaches zero of the change in position over the change in t.
Mathematically,
Where x is the given function with respect to time t. The Instantaneous Velocity is expressed in m/s.
Acceleration is the rate of change of velocity with time.It is a vector quantity.
Average acceleration is the change in velocity per unit time over an interval of time.
Let initial velocity at time interval t1 is v1 and final velocity at time interval t2 is v2
Then
instantaneous acceleration is measured over a "short" time interval. The word short in this context means infinitely small or infinitesimal — having no duration or extent whatsoever.
It's a mathematical ideal that can can only be realized as a limit. The limit of a rate as the denominator approaches zero is called a derivative.
Instantaneous acceleration is then the limit of average acceleration as the time interval approaches zero — or alternatively, acceleration is the derivative of velocity.
Consider a particle moving along a straight line with uniform acceleration 'a'. At t = 0, let the particle be at A and be its initial velocity and when t = t, v be its final velocity.
Acceleration =
=>
=>
initial velocity u = 60 m/s
As it stop final velocity v = 0
Time taken t = 4 s
We know,
Negative sign shows it is declaration.