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how can we find initial velocity and final velocity?

The three ways to calculate initial velocity
    1.Finding Initial Velocity with Final Velocity, Acceleration and Time
Equation used is v(i) = v(f) - a*t where 
v(i) - the initial velocity 
v(f) - the final velocity 
a  - the acceleration  and t - the time.

    2. Finding Initial Velocity with Distance, Time, and Acceleration
The necessary equation is: v(i) = (d / t) - [(a * t) / 2] where d stands for distance travelled.

    3. Finding Initial Velocity with Final Velocity, Acceleration and Distance
The correct equation is: v(i) = root [v(f) ^ 2 - (2 * a * d)]
The 1st and 3rd methods can be used to find final velocity when other components are given.
When average speed is known, average speed = 1/2 [ v(i) + v(f) ] .
When objects are dropped from different heights,the formula used to find final and initial velocity given only time and distance is 
1/2[v(f)]^2 - 1/2[v(i)]^2 = gH where
g is a constant = 9.8m/sec^2 (acceleration of gravity).
H is the height from which the object falls.



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