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Acceleration Calculator

Enter the required entities in the acceleration calculator and it will calculate the acceleration of an object or body based on the input parameters.

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To Calculate

The acceleration calculator computes the change in velocity of an object or body, or initial and final speed, or time to reach a given speed effortlessly. This acceleration finder uses different approaches like speed difference, constant acceleration, distance traveled over time, and constant acceleration methods to facilitate the acceleration-related calculations. 

Acceleration Formula:

It means to measure the rate of change in the speed of an object. As Newton's second law states “ the acceleration is directly proportional to the sum of the forces acting on an object and is inverse of the mass of the object”.  Let's take a look at the acceleration equations:

\(\ a = \dfrac{v_{f}-v_{i}}{Δt}\)

\(\ a =\ 2\times \dfrac{Δd − v_{i}\times Δt}{Δt^{2}}\)

\(\ a =\dfrac{F}{m}\)

Where:

  • a represents the acceleration
  • \(\ v_{i}\) and\(\ v_{f}\) are the initial and final velocities of the object
  • Δt is the time
  • Δd shows the distance traveled by the object
  • F is the net force that accelerates an object
  • m indicates the mass of the object

Equations For Initial Velocity, Final Velocity, And Time:

Use the below-mentioned formulas to find the initial velocity, final velocity, And time:

  • \(\ Initial\ Velocity\ (v_{0}) =\ v_{1}-\dfrac{a}{t}\)
  • \(\ Final\ Velocity\ (v_{1}) =\ v_{0}+\dfrac{a}{t}\)
  • \(\ Time\ (t) =\dfrac{v_{1} - v_{0}}{a}\)

Most often, initial velocity is used as the initial speed of the object or body. 

How To Calculate Acceleration?

There are three methods to calculate the acceleration that are: 

Using Velocities And Time Intervals:

  • Determine the change in velocities of the object during a specific time interval from t1 to t2.
  • The following equation calculates the acceleration in this case:
  • \(\ a = \dfrac{v_{f}-v_{i}}{Δt}\)

Force And Mass:

According to Newton’s law of motion, when a body accelerates a force is acting on it.

  • Measure the mass of the body or object
  • Determine the force acting on it The acceleration produced can be calculated by putting the values of mass and force in the following equation:
  • \(\ a =\dfrac{F}{m}\)

Using Velocity:

  • Determine the differentiating velocity vector with respect to time
  • Calculate the acceleration with the help of the relationship between velocity, time, and displacement as below:
  • \(\ a =\dfrac{dv}{dt}\)

Practical Example:

A train is running with a uniform velocity that is v = 5 m.s-1 and covers a distance. After 20 seconds, it stops accelerating and sustains a uniform velocity that is v = 25 m.s-1. Find acceleration.

Solution:

\(V_{i}=5m.s^{-1}\)

\(V_{f} = 25 m.s\)

\(T = 20 s\)

Put these values in one of the acceleration equations which requires the provided values:

\(\ a = \dfrac{v_{f}-v_{i}}{Δt}\)

\(a=\dfrac{25−5}{20}\)

\(a=1 m.s^{-2}\)

Keep in mind the changing of force brings changes in acceleration but the magnitude of the acceleration depends upon the mass of the object. The magnitude means how fast the object is accelerating. 

Terms Related To Acceleration:

Here we have provided an informational table that contains acceleration-related terms for a better understanding:

Terms Explanation
Positive: When the final velocity of the body or object is higher than the initial velocity.
Negative: When the final velocity is lower than the initial velocity, the acceleration is negative.
Centripetal Acceleration: If an object is moving in a circle then the acceleration experienced by the object is known as centripetal acceleration.
Linear: When a body or object is moving in a straight line, covering a distance and the motion is in one direction.
Instantaneous Acceleration: Measuring the acceleration of a body at a specific instant of time.
Acceleration Due To Gravity: A body that is falling freely experiences acceleration due to gravity because of the gravitational force of the Earth. The value of gravitational force is: \(\ 9.8\ ms^{-2}\).
Angular Acceleration: It is the rate of change of the angular velocity of an object or body. Meanwhile, it informs about how fast an object spins.

FAQ’s:

What Is The Difference Between Velocity And Acceleration?

Velocity means the change of displacement while acceleration is the change of velocity.

How Do You Find Angular Acceleration?

To calculate the angular acceleration use the following formula:

\(\ α =\dfrac{ω}{t}\)

Where

  • ω indicates the angular velocity 
  • t is the time

How Do You Calculate Average Acceleration?

Follow these steps:

  • Determine the change in velocity of an object when it’s in a state of motion and covering a distance
  • Find the change in time
  • Divide the change in velocity by the change in time

Can Acceleration Be Negative?

Yes, it can be negative and is termed as deceleration. For instance, when the break of a car is applied, then it stops because of negative acceleration. 

Is Acceleration A Vector?

Yes, because it has both direction and magnitude.

References:

From the source of Wikipedia, the free encyclopedia – Simple definition of acceleration (physics) along with the properties – units. From the source of WikiHow - Co-authored by Sean Alexander, MS - How to Calculate Acceleration (Methods).