final velocity

Meaning: Final velocity is the velocity at the end of the interval you are analyzing, compared with initial velocity v₀ at the start. Velocity is a vector, so direction matters: with up as positive, a ball thrown upward has a positive v₀ and acceleration of −g (about 9.8 m/s² downward near Earth's surface, with air resistance neglected). The kinematic equations below apply only when acceleration is constant.

Equation: v = v₀ + at, where v is final velocity (m/s), v₀ is initial velocity (m/s), a is constant acceleration (m/s²), and t is time (s). Also v² = v₀² + 2aΔx, where Δx is displacement (m). Without a time value, use the second form.

On the MCAT: Typical questions involve free fall, projectiles, or a block sliding down an incline. You are asked for the speed at impact, or for the final velocity after a given time. For projectiles, treat horizontal and vertical components separately: the horizontal component stays constant without air resistance, while the vertical component changes at g. Velocity-time graphs also appear, where the slope is acceleration and the area under the curve is displacement.

Common confusion: Final velocity is not always the maximum velocity, and it is not zero just because the object stops at the top of its path. At the peak the vertical component is zero, but the object is still accelerating at g. Also keep signs consistent: a downward final velocity with up defined as positive is negative.