كيفية الحساب التسارع (a = (v − u)/t)

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

What التسارع Asks

التسارع 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 الصيغةs

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.

التسارع vs السرعة المتجهة vs القوة

السرعة المتجهة 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.

حوّل minutes to seconds before substituting.

الشغلed 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.

أخطاء شائعة

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

التسارع calculator — a = (v − u)/t.

السرعة المتجهة calculator.

القوة calculator.

Kinematics calculator.

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

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