Acceleration
Acceleration is the rate of change of velocity with respect to time, and is a vector quantity. An object accelerates whenever its speed changes, its direction changes, or both simultaneously. Acceleration is caused by a net force (Newton's second law) and is measured in metres per second squared (m/s²).
Key Formula
a = (v_f − v_i) / t
LaTeX: \vec{a} = \frac{\Delta \vec{v}}{\Delta t} = \frac{\vec{v}_f - \vec{v}_i}{t}
| Symbol | Meaning | Unit |
|---|---|---|
| a⃗ | Acceleration | m/s² |
| v⃗_f | Final velocity | m/s |
| v⃗_i | Initial velocity | m/s |
| t | Time interval | s |
Worked Example
Problem
A motorcycle increases its velocity from 10 m/s to 40 m/s in 6 seconds. Calculate its average acceleration.
Solution
Step 1: Identify values: v_i = 10 m/s, v_f = 40 m/s, t = 6 s. Step 2: Apply the formula: a = (v_f − v_i) / t = (40 − 10) / 6 = 30 / 6 = 5 m/s².
Answer
Average acceleration = 5 m/s² in the direction of motion.
Types of acceleration in classical mechanics
| Type | Description | Example | Direction |
|---|---|---|---|
| Uniform acceleration | Constant rate of velocity change | Free fall near Earth | Constant direction |
| Non-uniform acceleration | Changing rate of velocity change | Car in city traffic | Varies |
| Deceleration (retardation) | Negative acceleration (slowing down) | Braking car | Opposite to velocity |
| Centripetal acceleration | Acceleration toward centre of circular path | Satellite in orbit | Toward centre |
| Tangential acceleration | Rate of speed change on a curved path | Speeding up on a curve | Along velocity |
Interactive Tools
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Related Terms
Velocity
Velocity is the rate of change of displacement with respect to time, making it a vector quantity with both magnitude (speed) and direction. Average velocity equals total displacement divided by total time, while instantaneous velocity is the derivative of position with respect to time. Velocity is central to Newton's laws and is measured in metres per second (m/s).
Free Fall
Free fall is the motion of an object under the influence of gravity alone, with no other forces such as air resistance acting on it. Near Earth's surface, all freely falling objects experience the same constant downward acceleration g ≈ 9.8 m/s², regardless of their mass — a result first demonstrated experimentally by Galileo Galilei. Free fall is a special case of uniformly accelerated motion.
Uniform Motion
Uniform motion is motion in which an object travels equal distances in equal intervals of time along a straight line, meaning its velocity is constant and its acceleration is zero. It is governed by Newton's first law (the law of inertia): in the absence of a net external force, a body in motion continues at constant velocity. The position-time graph for uniform motion is a straight line with constant slope.
From Latin "acceleratio" (a hastening), from "accelerare" — "ad-" (to) + "celerare" (to hasten), itself from "celer" (swift). Newton formalised the concept in the 1680s in "Philosophiæ Naturalis Principia Mathematica".