# How to Calculate Acceleration – 3 Formulas You Must Know

March 30, 2024

Every day you can experience differences in rates of acceleration whether you are aware of it or not. Take driving, for instance: when you hear a sports car rushing past you or a plane soaring past another one above you, you’re witnessing how acceleration changes in real-time. It’s a common mistake to confuse acceleration for speed or velocity, but the acceleration formula involves calculating the rate of change in the velocity of something as it moves over time. Therefore, in order to know how to calculate acceleration, you’ll need to know the velocity and set period of time.

Acceleration differs from velocity because velocity is the speed of an object in a given direction. The difference between the two is that to calculate acceleration, you need not just velocity but also time. Acceleration measures how much something is becoming faster or slower, depending on these factors. To calculate acceleration, you’ll have to familiarize yourself with challenging math formulas that are prevalent in physics.

Here are 3 acceleration formulas you must know:

## 1) Calculating the average acceleration from two velocities and two points in time

The arguably most widely used acceleration formula is as follows:

a = △v / △t

Here, △v is the change in velocity and △t is the change in time. Looking at it more closely, the equation can also be written as:

a = [v(f) – v(i)] / [t(f) – t(i)]

In this acceleration formula, you are calculating the difference in final and initial velocity with final and initial time, where v(f) is the final velocity, v(i) is the initial velocity, t(f) is the final time and t(i) is the initial time. It is crucial to always subtract the initial velocity or time from the final velocity or time, and not the other way around. Switching these can result in an incorrect direction of your acceleration. Bear in mind that it’s still okay if your final time (t(f)) is smaller than your initial time (t(i)) because this just means that you will have a negative acceleration, which translates into “you’re slowing down.” And if, for some reason, you do not have a starting time (initial time), then you can plug in “0” as t(i).

### How to Calculate Acceleration Formulas (Continued)

This acceleration formula of change in velocity over change in time can also be applied in the angular acceleration formula. The angular acceleration formula calculates the rate the angular acceleration of a rotating object changes with respect to time. Similar to the average acceleration formula we saw above, this formula is written as:

a = (change in angular velocity) / (change in time)

## 2) How to calculate acceleration using Newton’s second law of motion

Another way to figure out how to calculate acceleration is through Newton’s second law of motion, which states that an object will accelerate when the forces acting upon it are unbalanced. Acceleration here is contingent on the mass of an object and the net forces acting upon it. In a nutshell, Newton’s law points out that acceleration can be calculated if you know the force that is acting on the object. The acceleration formula is as follows:

F(net) = m x a

### How to Calculate Acceleration Formulas (Continued)

Here, F(net) represents the total force that is acting on the object, while m represents the mass of the object and a represents the acceleration of the object. To know how to calculate acceleration for Newton’s second law of motion, it’s required to use units in the metric system, which means that you must use newtons (N) for force, kilograms (kg) for mass and meters per second squared (m/s2) for acceleration.

1) To find the mass of the object, you are going to weigh the object in order to identify its mass in grams. Utilizing a scale or a balance is the ideal method, and the larger object you use, the greater the chances are that the mass will be measured in kilograms. To convert the mass of an object into kilograms from grams, you just need to divide the mass by 1000.

### How to Calculate Acceleration Formulas (Continued)

2) To find the net force acting on an object, you will have to look at the unbalanced forces at play. If one force is larger than the other, then the resulting net force will go in the direction of the larger force. In this example, because acceleration occurs when the unbalanced force impacts an object, the object will go in the direction that is more powerful. The units used when calculating the net force is by newton (N). So it’s important to know that 1 newton (N) is equivalent to 1 kilogram (kg) x meter/second squared (m/s2).

For example, if a larger dog and a smaller dog are both pulling at the same toy, but the larger dog is pulling with a force of 6 newtons and the smaller dog is pulling with a force of 4 newtons, then the net force will be 2 newtons going in the direction of the larger dog, from where the larger dog has been pulling.

3) Find the acceleration by reordering Newton’s second law of motion. With the acceleration formula of F(net) = m x a, you can calculate for acceleration by dividing the two sides by mass (m). This essentially means that you’ll have to divide the net force by the mass of the object in order to calculate the acceleration, which results in the following equation:

a = F(net) / m

Some things to keep in mind here are that force is directly proportional to acceleration, while mass does the exact opposite in how it is inversely proportional. This means that with a greater force, you can expect a greater acceleration. And with a greater mass, you can expect a lower (decreasing) acceleration.

## 3) Utilizing distance traveled during acceleration

Take a look at the following acceleration formula that uses distance:

a = 2 × (Δd − v(i) × Δt) / Δt²

Here, like in the aforementioned formulas above, a represents acceleration, v(i) represents the initial velocity, and Δt represents acceleration time and Δd represents the distance traveled during acceleration time.

## Further examples of acceleration

How do you calculate acceleration when an object is moving inwards towards the center of a circle, like Earth? Centripetal acceleration. It can change the direction of the velocity, and as a result, the shape of its course, but it does not affect the value of the velocity. Due to the gravity of the sun, the Earth has centripetal acceleration and moves at a constant value, although the speed does change here and there throughout the year. The centripetal acceleration formula calculates the rate of the object’s motion that moves in such a manner. The centripetal acceleration equation is as follows:

a(c) = v2/ r

In this acceleration formula, you have a(c) which represents acceleration (centripetal), v which represents velocity and r which represents radius.

Other examples of acceleration include angular acceleration, mentioned earlier above, and gravitational acceleration, which is the acceleration of an object in free fall within a vacuum.

## Comprehending the key elements of the acceleration formula

It’s one thing to memorize these three formulas, and another thing to actually understand them. Some of the most interesting research topics involve understanding acceleration. When you’re learning how to calculate acceleration, take the time you need to understand the following elements:

A. The direction of force
A force can only cause acceleration in the direction the force is going in. If, for example, you are solving a problem that tells you that a miniature plane with a mass of 20 kg is accelerating south at 4 m/s2 and there is a wind blowing east at 100 Newtons, what is the car’s acceleration? Since the force of the wind blowing against the car is perpendicular to its southbound direction, the miniature plane will continue accelerating south at 4 m/s2.

### How to Calculate Acceleration Formulas (Continued)

1) Net force

Always make sure to check if there is more than one force acting on the object, and if there is, then combine the forces into a net force. Forces could be going in the same direction or opposite directions, so you’ll need to calculate the net force to end up with the accurate acceleration.

2) The direction of acceleration

It’s important to remember that the direction of acceleration might not correspond to our usual understanding of it in our daily lives. Take for instance the example of driving a car. The direction of acceleration is usually positive if it is moving up or right, and negative if moving down or left. A driver moving right and pressing on the gas pedal will result in a positive direction of acceleration; a driver moving right and pressing on the brakes will result in a less positive velocity, therefore creating a negative direction of acceleration.

## How to Calculate Acceleration Formulas – Tip of the iceberg

The more you learn about acceleration, the more you’ll come across formulaic rules that might remind you of certain formulas on SAT/ACT math sections or natural log rules. That’s because these mathematical formulas are foundational to understanding the mechanics of such matters in physics. When you learn how to calculate acceleration, you’ll be stepping into a world, if not worlds, of equations that seek to explain the nature of motion.

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