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Acceleration Formula to Help You Get Through Your Physics Lessons

Omkar Phatak Jun 3, 2019
If you need to know the formula for acceleration of a particle, this post will help you out. Read to get a hang of what acceleration means and understand how it is intimately connected with the concept of force.
When taking a basic physics course, one of the most important concepts that you need to understand is acceleration. That is because understanding acceleration is intimately connected with comprehending what a force is.
Acceleration is not an abstract concept. In fact, it is something that we readily feel in our daily life when traveling in a car, diving in the swimming pool from high up, and during many other such instances.

What is Acceleration?

To understand what acceleration is, recall the experience of traveling in a car. To make a car move, a driver pushes on the accelerator pedal and it starts moving. As it moves, you observe the speedometer needle in the dashboard gauge rising and turning clockwise towards the right.
What is happening? The velocity of the car is changing with time. So acceleration is simply the change in velocity of the car. Velocity is a vector quantity, that specifies the direction in which an object is moving, along with the speed (magnitude of velocity).
How is acceleration connected with force? It is in the very definition of force. Recall Newton's laws of motion. The first laws states that any object left undisturbed, continues in its state of rest or uniform motion.
The second law, which contains the definition of force, indirectly states that the magnitude of force applied is directly proportional to the rate of change of velocity or acceleration of an object. Any type of force causes a change in the velocity of an object. Even if the direction of velocity is changed, a force has acted.
Acceleration is the rate of change velocity with time. Force manifests itself by changing an object's velocity. If you look around, you will find many examples of acceleration and every one of them is due to the action of either the gravitational or electromagnetic forces.

General Formula For Acceleration

The formula for acceleration can be easily calculated by pure deduction from its definition as the rate of change of velocity. The formula for average acceleration that provides the value over an extended period of time is as follows:

Average Acceleration = ΔV/ΔT

where ΔV is the change in velocity and ΔT is the change in time.
The formula for instantaneous acceleration, which provides a value at every point of time is as follows:

Instantaneous Acceleration = dV/dt = d2R / dt2

where V is the velocity vector and R is the displacement vector.

The unit of acceleration is meters / second2, according to the SI system.

The Formula Derived From Newton's Law

The formula for acceleration can be derived from the Newton's second law of motion. The mathematical statement of the Newton's law of motion is as follows:

F = ma

where F is the force, m is the mass of the object, and a is the acceleration.
Therefore, when the force exerted on an object and its mass is known, one can easily calculate the acceleration using the following formula:

Acceleration (a) = F / m

This formula is simply a restatement of Newton's second law.