Question

First half of a velocity is covered with derivation

Answer 1

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Basis for velocity-time derivations

The derivations start with the assumption that the acceleration due to gravity g is a constant for displacements relatively close to Earth.

Acceleration is also the incremental change in velocity with respect to time:

a = dv/dt

where

a is the accelerationdv is the first derivative of velocity v (a small change in velocity)dt is the first derivative of time t (a small time increment)Note: Vectors have magnitude and direction and are indicated in boldface. Scalars have only magnitude and are in regular text.(See Vectors in Gravity Equations for more information.)

Since g is the acceleration due to gravity:

a = g

and

dv/dt = g

Multiply both sides of the equation by dt to get:

dv = g*dt

By using Calculus to integrate this equation, you can get the equations for velocity and time.

Velocity-time relationship

Derivation of velocity for a given time

Integrate dv = g*dt on both sides of the equal sign.

First, integrate dv over the interval from v = vi to v = v:

∫dv = v − vi

where

∫ is the integral sign, as used in Calculusv is the vertical velocity of the objectvi is the initial vertical velocity of the object

Note: The initial velocity is the velocity at which the object is released after being accelerated from zero velocity. Initial velocity does not occur instantaneously.

Then, integrate g*dt over the time interval from t = 0 to t = t:

∫g*dt = gt − 0

The result of the two integrations is:

v − vi = gt

Thus, the general gravity equation for velocity with respect to time is:

v = gt + viDerivation of time for a given velocity

The time it takes to reach a given velocity is obtained by rearranging the equation v = gt + vi and solving for t:

v − vi = gtt = (v − vi)/gSummary

Starting with the fact that the acceleration due to gravity g is considered a constant and knowing that acceleration is the change in velocity for a change in time, you can derive the gravity equations for the velocity with respect to time. You can then determine the equation for the time to reach a given velocity.

The derived equations are:

v = gt + vit = (v − vi)/gPlz mark  my brainlist

Answer 2

check Ur question properly and repost it...not able to understand