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Acceleration

General

Acceleration (Physics)

The rate of change of velocity with respect to time, calculated as a = (v_f − v_i) ÷ t, a vector quantity measured in meters per second squared.

Definition

Acceleration is the rate of change of velocity with respect to time. It captures not just speeding up, but any change in motion — slowing down (deceleration) and changing direction both count as acceleration, since velocity is a vector with both magnitude and direction. The Acceleration Calculator computes this value directly from initial velocity, final velocity, and elapsed time.

Because acceleration is derived from Velocity, it is also a vector quantity: its direction indicates whether an object is speeding up (acceleration in the same direction as motion) or slowing down (acceleration opposite to motion). A car braking to a stop and a car speeding up both have nonzero acceleration, just pointing in opposite directions relative to the car's motion, as explored further using the Velocity Calculator.

Acceleration is central to Newton's Second Law, which states that the net force on an object equals its mass times its acceleration (F = ma). This means acceleration is not just a description of motion but a direct consequence of the forces acting on an object — the greater the net force relative to mass, the greater the acceleration produced.

Formula

a = (v_f − v_i) ÷ t

Where a is acceleration (in meters per second squared, m/s²), v_f is final velocity, v_i is initial velocity (both in meters per second, m/s), and t is the time elapsed (in seconds, s).

Worked Example

A cyclist speeds up from an initial velocity of 4 m/s to a final velocity of 12 m/s over 8 seconds. Their acceleration is:

a = (v_f − v_i) ÷ t = (12 − 4) ÷ 8 = 8 ÷ 8 = 1 m/s²

This means the cyclist's velocity increases by 1 meter per second, every second, for the full 8 seconds. Using Newton's Second Law, if the cyclist and bike together have a mass of 75 kg, the net forward force required is F = m × a = 75 × 1 = 75 N.

Key Things to Know

  • Measures the rate of change of Velocity: not just how fast an object is moving, but how quickly that speed or direction is changing.
  • Deceleration is still acceleration: slowing down is described by the same formula, just with a negative result relative to the direction of motion.
  • Directly proportional to net force: Newton's Second Law shows that acceleration equals force divided by mass (a = F/m), so a bigger push or a lighter object both increase acceleration.
  • Gravity produces constant acceleration: near Earth's surface, free-falling objects accelerate downward at approximately 9.8 m/s², regardless of their mass (ignoring air resistance).
  • Direction matters as much as magnitude: two objects can have the same numerical acceleration but be speeding up or slowing down depending on how that acceleration compares to their current direction of motion.

Related Calculators

Acceleration Calculator →Calculate acceleration from initial velocity, final velocity, and time. Get instant results in m/s², plus the change in velocity, with a step-by-step breakdown shown.
Velocity Calculator →Calculate velocity from displacement and time, with direction shown instantly. Unlike speed, velocity is a vector — enter a signed displacement to see forward or backward motion.

Related Terms

VelocityVelocity (Physics)Newton's Second LawNewton's Second Law of Motion

Frequently Asked Questions

Acceleration measures how quickly an object's velocity is changing, whether it's speeding up, slowing down, or changing direction. A car that goes from 0 to 100 km/h quickly has a higher acceleration than one that takes much longer to reach the same speed.
Acceleration is measured in meters per second squared (m/s²) in the SI system, representing how many meters per second the velocity changes each second. Other common units include kilometers per hour per second and feet per second squared.
Deceleration (slowing down) is a type of acceleration where the acceleration vector points opposite to the direction of motion, which is often described as negative acceleration relative to a chosen positive direction. Mathematically it's calculated with the same formula, a = (v_f − v_i)/t, just with a negative result.
On Earth's surface, objects in free fall (ignoring air resistance) accelerate downward at approximately 9.8 m/s², often written as g. This means a falling object's downward velocity increases by about 9.8 m/s for every second it falls.
Newton's Second Law states that force equals mass times acceleration (F = ma), meaning acceleration is directly proportional to the net force applied to an object and inversely proportional to its mass. This is why the same push produces much less acceleration on a heavy object than a light one.