What is the formula for acceleration and deceleration?

Acceleration and deceleration share the same fundamental formula a = (v - u) / t, with deceleration simply being negative acceleration—acceleration in the direction opposite to motion. The sign of your result indicates whether the object is speeding up (positive) or slowing down (negative), determined by your chosen coordinate system. If you define forward as positive and a car slows from 25 m/s to 10 m/s in 5 seconds, a = (10-25)/5 = -3 m/s², which represents deceleration.

The mathematical treatment remains identical regardless of whether velocity increases or decreases; physics doesn't have separate deceleration equations. What changes is your interpretation of the sign and your chosen reference direction. In braking scenarios, engineers often flip the sign to report deceleration as a positive value because it's more intuitive for safety ratings ("this car can decelerate at 8 m/s²" sounds clearer than "acceleration of -8 m/s²"). Just ensure your entire problem maintains consistent sign conventions.

Real applications frequently involve both acceleration and deceleration in sequence. A subway train accelerates at 1.2 m/s² for 20 seconds, travels at constant velocity, then decelerates at -1.5 m/s² for 15 seconds. Calculating each phase separately using the same formula structure—then combining the results—describes the complete motion profile. For velocity-squared formulas like a = (v²-u²)/2s, deceleration automatically appears as negative when v < u, so you don't need separate equations—just careful attention to which velocity is initial and which is final.