Acceleration Formula: a = (v − u)/t, SI Unit and Examples

The acceleration formula is $a = \frac{v - u}{t}$ : take the final velocity, subtract the initial velocity, and divide by the time the change took. The answer tells you how many metres per second the velocity changes in every second, which is why the SI unit is metres per second squared (m/s²).

Indian textbooks write u for initial velocity and v for final velocity. Many US books write the same idea as $a = \frac{\Delta v}{\Delta t}$ or $a = \frac{v_f - v_i}{t}$ . It is one formula with three spellings, so use whichever your teacher uses and keep it consistent. Acceleration is a kinematics quantity that builds directly on velocity.

Quick facts

Formula
$a = \frac{v - u}{t}$
SI unit
metre per second squared (m/s²)
Dimensional formula
[M⁰ L¹ T⁻²]
Type
Vector: it has a size and a direction
With force
$a = \frac{F}{m}$ from Newton's second law
Negative value
Slowing down in the chosen positive direction, also called retardation or deceleration

What each symbol in the acceleration formula means

Symbols in a = (v − u) / t
Symbol	Meaning	SI unit
$a$	Acceleration, the rate of change of velocity	m/s²
$v$	Final velocity at the end of the time interval	m/s
$u$	Initial velocity at the start of the interval	m/s
$t$	Time taken for the velocity to change	s

The top of the fraction, $v - u$ , is the change in velocity. It is not the speed at any one moment. A bus that goes from 10 m/s to 16 m/s has a change of 6 m/s, and if that took 3 s the acceleration is 2 m/s². Velocity has a direction, so a change in direction at constant speed is also a change in velocity. That is why a car taking a bend at steady speed is still accelerating, a case covered by the centripetal acceleration formula.

How to use the formula in four steps

Pick a positive direction. Usually the direction the object starts moving. Anything moving the other way gets a minus sign.
Convert units first. Change km/h to m/s by dividing by 3.6, and minutes to seconds by multiplying by 60.
Substitute with signs. Write $a = \frac{v - u}{t}$ and put each value in with its sign and unit.
Read the sign of the answer. A positive a points in your positive direction. A negative a points the other way, which for a forward moving object means it is slowing down.

The calculator above follows the same steps. Enter any three values in SI units and it solves for the fourth, so you can check your homework line by line.

Worked examples

Example 1: a cyclist speeding up

A cyclist goes from 2 m/s to 8 m/s in 4 s. Find the acceleration.

Given: u = 2 m/s, v = 8 m/s, t = 4 s.

$a = \frac{8 - 2}{4} = \frac{6}{4} = 1.5\ \text{m/s}^2$

The cyclist gains 1.5 m/s of speed every second.

Example 2: braking with a unit conversion

A car moving at 72 km/h brakes to rest in 5 s. Find its acceleration.

Convert first: 72 ÷ 3.6 = 20 m/s, so u = 20 m/s, v = 0, t = 5 s.

$a = \frac{0 - 20}{5} = -4\ \text{m/s}^2$

The minus sign means the acceleration points backwards. The retardation is 4 m/s².

Example 3: finding the time

A lift accelerates upward at 1.2 m/s² from rest. How long does it take to reach 3 m/s?

Rearrange: $t = \frac{v - u}{a} = \frac{3 - 0}{1.2} = 2.5\ \text{s}$

Other forms of the acceleration formula

The basic form needs a time. When the question gives something else, one of these forms fits better:

Which acceleration formula to use
You know	Use
u, v and t	$a = \frac{v - u}{t}$
u, v and distance s	$a = \frac{v^2 - u^2}{2s}$
u, s and t	$a = \frac{2(s - ut)}{t^2}$
Net force F and mass m	$a = \frac{F}{m}$
Radius r and speed v on a circle	$a = \frac{v^2}{r}$

The middle three rows come from the equations of motion and only hold when acceleration is constant. The force form is Newton's second law; see the force formula page for F = ma itself. Over a longer trip where the acceleration changes, the same fraction gives the average acceleration.

Units, dimensions and the velocity time graph

Dividing m/s by s gives m/s², read as metres per second per second. In base dimensions that is length over time squared, so the dimensional formula of acceleration is [M⁰ L¹ T⁻²]. Any formula for a must reduce to these dimensions, which is a quick way to catch a slip in a rearrangement.

On a velocity time graph, acceleration is the slope. A straight line rising to the right means constant positive acceleration, a flat line means zero acceleration, and a line falling to the right means negative acceleration. The area under the same graph gives the displacement, which links this page to the displacement formula.

Common mistakes that cost marks

Mixing km/h and m/s. Convert every speed to m/s before you substitute.
Swapping u and v. It is always final minus initial. Reversing them flips the sign of the answer.
Dropping the minus sign. If the question asks for retardation, give the size without the sign. If it asks for acceleration, keep the sign.
Calling zero velocity zero acceleration. A ball at the top of a vertical throw has v = 0 for an instant, but its acceleration is still 9.8 m/s² downward.

Quick check: the free fall acceleration near Earth is about 9.8 m/s². An answer far above that for a car or a person running usually means a unit was not converted.

Frequently asked questions

What is the formula of acceleration in physics?

Acceleration equals the change in velocity divided by the time taken: a = (v − u) / t. With a known net force, you can also use a = F / m.

What is the SI unit of acceleration?

The SI unit is metre per second squared, written m/s². It means the velocity changes by that many metres per second every second.

Is acceleration a vector or a scalar?

Acceleration is a vector. It has a size and a direction, which is why a negative value means it points opposite to the direction you chose as positive.

How do you find acceleration with distance and velocity only?

Use the third equation of motion, v² = u² + 2as, rearranged to a = (v² − u²) / 2s. It works when the acceleration is constant and you know the distance instead of the time.

What is the difference between acceleration and velocity?

Velocity is how fast and in which direction position changes, in m/s. Acceleration is how fast velocity itself changes, in m/s². An object can have a large velocity and zero acceleration if it moves steadily in a straight line.