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 standard formula for average acceleration is expressed as:

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.

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).

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.

1. Identify the initial velocity: The motorcycle starts from a standstill, so v_i = 0 m/s.
2. Identify the final velocity: v_f = 30 m/s.
3. Identify the elapsed time: t = 5 s.
4. Set up the equation: a = (30 − 0) / 5.
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.

• 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.

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.