Equation of motion : velocity-time
This equation of motion are valid only when acceleration is constant and motion is constrained to a straight line.
The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. The longer the acceleration, the greater the change in velocity. Change in velocity is directly proportional to time when acceleration is constant. If velocity increases by a certain amount in a certain time, it should increase by twice that amount in twice the time. If an object already started with a certain velocity, then its new velocity would be the old velocity plus this change.
Derivation:
Equation of acceleration
\[a = \frac{\bigtriangleup V}{\bigtriangleup t} \]
Expand Δv to v − v0 and condense Δt to t.
\[a = \frac{v - v_{0}}{t} \]
Then solve for v as a function of t.
\[v = v_{0} + at \]
