How to Calculate Acceleration (a = (v − u)/t)

Calculate average acceleration with a = (v − u)/t. Signs, deceleration, rearrangements, worked examples, and a free acceleration calculator.

What Acceleration Asks

Acceleration is how quickly velocity changes. A car can be fast and still have zero acceleration if its speed stays constant. Speeding up, slowing down, or changing direction all mean non-zero acceleration.

Average acceleration over a time interval is a = (v − u) / t. Final velocity v minus initial velocity u, divided by time t. Units are m/s² when velocities are in m/s and time is in seconds.

If you already have u, v, and t (or a and one unknown), open the free acceleration calculator first, then return here for signs, deceleration, and SUVAT links.

The Formulas

  • a = (v − u) / t — average acceleration.
  • v = u + at — rearrange for final velocity.
  • u = v − at — rearrange for initial velocity.
  • t = (v − u) / a — rearrange for time.

    • These forms assume constant (or average) acceleration over the interval. If acceleration changes with time, you need more advanced kinematics or calculus.

    Signs and Deceleration

  • Pick one direction as positive (usually the initial motion).
  • Speeding up in the positive direction → a > 0.
  • Slowing down (braking) while moving positive → a < 0 (deceleration).
  • A negative a does not always mean “going backward” — it means velocity is becoming less positive.

    • Acceleration vs Velocity vs Force

    Velocity says how fast and which way you move. See velocity for v = d/t when acceleration is not needed.

    Net force causes acceleration: F = ma. Once you have a, use the force calculator.

    When more than two of s, u, v, a, t are known under constant a, use the kinematics calculator or the

    SUVAT choice guide.

    Units

  • u, v → m/s (divide km/h by 3.6).
  • t → seconds.
  • a → m/s².
  • Convert minutes to seconds before substituting.

    • Worked Examples

    Example 1: 0 to 20 m/s in 5.0 s

    a = (v − u)/t = (20 − 0)/5.0 = 4.0 m/s².

    Example 2: braking

    u = 25 m/s, v = 5.0 m/s, t = 4.0 s. a = (5 − 25)/4 = −5.0 m/s² (deceleration of 5.0 m/s²).

    Example 3: find final velocity

    u = 10 m/s, a = 2.0 m/s², t = 6.0 s. v = u + at = 10 + (2)(6) = 22 m/s.

    Example 4: find time

    u = 0, v = 15 m/s, a = 3.0 m/s². t = (v − u)/a = 15/3.0 = 5.0 s.

    Common Mistakes

  • Leaving km/h in a = (v − u)/t without converting to m/s.
  • Using minutes for t while velocities are in m/s.
  • Dropping the minus sign when an object slows down.
  • Confusing high speed with high acceleration.

    • Check It on the Calculator

    Acceleration calculator — a = (v − u)/t.

    Velocity calculator.

    Force calculator.

    Kinematics calculator.

    Learn a = (v − u)/t and confirm every homework number on the calculator.

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