The final velocity of a moving object can be found using one of the following common formulas, depending on what information is available:
- When initial velocity, acceleration, and time are known:
vf=vi+a⋅tv_f=v_i+a\cdot tvf=vi+a⋅t
where vfv_fvf is the final velocity, viv_ivi is the initial velocity, aaa is acceleration, and ttt is the time during which the acceleration acts.
- When initial velocity, acceleration, and displacement (distance moved) are known but time is unknown:
vf=vi2+2asv_f=\sqrt{v_i^2+2as}vf=vi2+2as
where sss is the displacement. These formulas assume constant acceleration during the motion. The first formula calculates final velocity by adding the change in velocity (acceleration times time) to the initial velocity. The second formula relates velocity to displacement when time is not available. Typical units are meters per second (m/s) for velocities, meters (m) for displacement, seconds (s) for time, and meters per second squared (m/s²) for acceleration. For example, if an object starts at 50 m/s, accelerates at 5 m/s² for 5 seconds, its final velocity would be:
vf=50+5×5=75 m/sv_f=50+5\times 5=75\text{ m/s}vf=50+5×5=75 m/s
Alternatively, if displacement and acceleration are known, the second formula can be used directly without time. These formulas are fundamental in physics for analyzing motion under constant acceleration.
