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Acceleration Formula
Acceleration is the rate at which an object changes its velocity. It is a fundamental concept in physics and mechanics that explains how things speed up, slow down, or change direction. Understanding how to use the acceleration formula helps you solve motion problems in school, physics labs, and engineering. For a fast calculation, use the acceleration calculator to solve for acceleration, time, or velocity.
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What is the acceleration formula?
The average acceleration formula calculates the change in velocity over a specific period of time. Because it is a rate of change, it tells you how much the velocity changes each second.
Like velocity, acceleration is a vector quantity. This means it has both a magnitude (how much the speed is changing) and a direction (where the change is pushing the object).
The acceleration formula
The standard formula for average acceleration is expressed as:
The acceleration formula
a = (v_f − v_i) / t
The variables
- a = average acceleration
- v_f = final velocity
- v_i = initial velocity
- t = time taken for the velocity to change
The top part of the formula, (v_f − v_i), determines the total change in velocity. The bottom part, t, averages this change over the elapsed time.
Understanding acceleration units
Because acceleration is velocity divided by time, its unit is a velocity unit divided by a time unit. The standard International System of Units (SI) unit is:
meters per second squared (m/s²)
This unit means "meters per second, per second." For example, an acceleration of 3 m/s² means that the object's velocity increases by 3 meters per second every single second.
In the imperial system, acceleration is typically measured in feet per second squared (ft/s²) or miles per hour per second (mph/s).
Worked example: Calculating acceleration
Let's calculate the acceleration of a motorcycle that starts from a standstill and speeds up to a velocity of 30 m/s in exactly 5 seconds.
- Identify the initial velocity: The motorcycle starts from a standstill, so v_i = 0 m/s.
- Identify the final velocity: v_f = 30 m/s.
- Identify the elapsed time: t = 5 s.
- Set up the equation: a = (30 − 0) / 5.
- Calculate: a = 30 / 5 = 6 m/s².
The motorcycle's average acceleration is 6 m/s². This means its speed increased by 6 meters per second every second during its acceleration.
Common acceleration mistakes
- Mixing up initial and final velocity. If an object slows down, its final velocity is smaller than its initial velocity. Mixing these up will result in a positive acceleration instead of a negative deceleration.
- Unit mismatch. If you have speed in miles per hour and time in seconds, you must convert the speed unit to feet per second or miles per second before dividing by time.
- Confusing acceleration with velocity. An object can have a high velocity but zero acceleration if it is moving at a constant speed in a straight line.
Acceleration vs. Velocity
To understand motion clearly, you must differentiate between velocity and acceleration:
- Velocity measures how far an object travels in a given amount of time (e.g., 60 mph North).
- Acceleration measures how fast the velocity changes (e.g., speeding up from 50 mph to 60 mph).
If you are driving a car at a steady 70 mph on a straight highway, your velocity is 70 mph, but your acceleration is exactly 0. For more on calculating speed and distance, see the velocity calculator.
Run the numbers
Explore physics and motion calculators to check your work and understand kinematics:
Acceleration Calculator
Calculate average acceleration, final velocity, initial velocity, or time with automatic unit conversions.
Velocity Calculator
Solve for average velocity, displacement, or time given the other variables.
Time Calculator
Find elapsed durations, add or subtract time units easily.
Frequently asked questions
Acceleration is the rate at which an object changes its velocity. Because velocity has both a speed and a direction, acceleration occurs whenever an object speeds up, slows down, or changes direction.
Speed is a scalar quantity indicating how fast an object is moving (e.g., 60 mph). Velocity is a vector quantity that includes both speed and direction (e.g., 60 mph North). Acceleration is based on changes in velocity.
Deceleration is acceleration in the opposite direction of the velocity vector, which causes an object to slow down. Mathematically, it is represented as a negative acceleration value.
On Earth, objects in free fall experience a constant acceleration due to gravity, denoted as g. Near the surface, g is approximately 9.8 m/s² (or 32.2 ft/s²), directed downward.
The acceleration calculator takes your initial velocity, final velocity, and time values to compute the average acceleration, automatically matching and converting speed units to prevent manual errors.