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Acceleration Calculator and Formula

The acceleration formula is a = (v − u)/t: acceleration = change in velocity ÷ time taken, with velocities in m/s, time in seconds and acceleration in m/s². A negative answer means the object is slowing down.

Acceleration formula: a = (v − u)/t

a = v − ut
a = v − utv = u + a·tu = v − a·tt = v − ua
a
acceleration, m/s²
v
final velocity, m/s
u
initial velocity, m/s
t
time, s

Convert every value to SI units (m, s, kg, A, V, Ω) before substituting into the formula. The calculator does this for you and shows the conversion as a step.

2 m/s²m/s²
aacceleration
2 m/s²
acceleration: 2 m/s²
The speedometer needle rises from 0 m/s to 20 m/s in 10 s. On the velocity–time graph, the gradient of the line is the acceleration, 2 m/s².

Step-by-step solution

  1. Formulaa = v − ut
  2. Substitutea = 20 m/s − 0 m/s10 s
  3. Answera = 2 m/s²

Acceleration examples

  1. Example 1

    A sports car accelerates along a straight road from 0 m/s to 30 m/s in 6 s. Calculate its acceleration.

    Given:u = 0 m/sv = 30 m/st = 6 s
    1. Formulaa = v − ut
    2. Substitutea = 30 m/s − 0 m/s6 s
    3. Answera = 5 m/s²

  2. Example 2

    A ball is moving at 4 m/s when it starts to roll down a slope, where it accelerates uniformly at 2 m/s². Calculate its velocity after 3 s.

    Given:u = 4 m/sa = 2 m/s²t = 3 s
    1. Formulav = u + a·t
    2. Substitutev = 4 m/s + 2 m/s² · 3 s
    3. Answerv = 10 m/s

  3. Example 3

    A driver brakes, and the car slows down from 25 m/s to 5 m/s in 4 s. Calculate the acceleration of the car.

    Given:u = 25 m/sv = 5 m/st = 4 s
    1. Formulaa = v − ut
    2. Substitutea = 5 m/s − 25 m/s4 s
    3. Answera = −5 m/s²

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What does acceleration mean?

Acceleration is the rate of change of velocity: how much the velocity changes each second. At GCSE it is written acceleration = change in velocity ÷ time taken, or a = Δv/t. With u for the initial velocity and v for the final velocity, Δv = v − u, so a = (v − u)/t. Velocity is in m/s and time is in s, so acceleration is in metres per second squared, m/s².

An acceleration of 3 m/s² means the velocity increases by 3 m/s every second. If the object slows down, v is smaller than u and the acceleration is negative, which is often called deceleration. The formula gives the average acceleration over the time interval and describes the motion exactly only when the acceleration is uniform. On a velocity–time graph the acceleration is the gradient of the line.

A real-life picture: a car pulling away from traffic lights gains speed quickly, while a train accelerates far more gently but for much longer. An object falling freely near the Earth's surface accelerates at about 9.8 m/s², as long as air resistance is small enough to ignore.

Common mistakes

  • Subtracting the wrong way round: the change in velocity is final minus initial, v − u, so braking gives a negative answer.
  • Forgetting to convert km/h to m/s before dividing by a time in seconds.
  • Dropping the minus sign for a deceleration, or giving a positive acceleration for an object that is slowing down.
  • Writing the unit as m/s instead of m/s².
  • Dividing the final velocity by the time when the object did not start from rest. Always use the change in velocity.

Related formulas

Speed, distance and timeSUVAT equationsKinetic energyAll physics equations

Frequently asked questions

Acceleration = change in velocity ÷ time taken, or a = (v − u)/t, where u is the initial velocity, v the final velocity and t the time. The unit is m/s².

Metres per second squared, m/s². It tells you by how many metres per second the velocity changes in each second.

Yes. A negative acceleration means the velocity is decreasing in the direction you have chosen as positive, for example when a car brakes. This is often called deceleration.

Find the gradient of the line by dividing the change in velocity by the time taken. A steeper line means a greater acceleration, and a horizontal line means a constant velocity.

Near the Earth's surface a freely falling object accelerates at about 9.8 m/s² if air resistance is negligible. Exam questions tell you which value of g to use.