How am I supposed to calculate the final velocity when I have initial velocity, acceleration, and time?

Calculating final velocity from initial velocity, acceleration, and time uses the straightforward linear equation v = u + at, where you add the velocity gained from acceleration (at) to the starting velocity (u). If a bicycle starts at 5 m/s and accelerates at 2 m/s² for 8 seconds, the final velocity is v = 5 + 2(8) = 5 + 16 = 21 m/s. The simplicity of this formula makes it the most frequently used in introductory physics, yet errors still occur when students forget to add the initial velocity or mishandle negative accelerations (deceleration).

For deceleration problems, the acceleration value is negative, which automatically reduces velocity. A car traveling at 30 m/s that brakes at -5 m/s² for 4 seconds reaches v = 30 + (-5)(4) = 30 - 20 = 10 m/s. If braking continued for 7 seconds, v = 30 - 35 = -5 m/s would mathematically indicate the car reversed direction—physically impossible for a braking vehicle, signaling the car actually stopped earlier. Always check whether calculated velocities make physical sense for your scenario.

This equation works equally well for multi-stage motion by applying it sequentially. A rocket accelerates at 15 m/s² for 10 seconds from launch (v₁ = 0 + 150 = 150 m/s), then at 8 m/s² for another 20 seconds (v₂ = 150 + 160 = 310 m/s). Breaking complex motion into constant-acceleration phases, then chaining calculations together, describes realistic scenarios where acceleration varies by stage. Document each phase clearly with subscripts or labels to avoid confusing intermediate values with final results.