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Acceleration Calculator

What is acceleration?

Acceleration is the rate of change of velocity of a moving body with time. When a body is moving and suddenly it changes its velocity, it is said to be accelerated. 

An important note:

Acceleration should be discussed in terms of velocity but not just speed. As we know, speed and velocity are two different concepts. Speed is a scalar quantity, while velocity is a vector. When you mention that the speed of a car is 100kmph, you do not know in which direction it is moving. But when you say in terms of velocity vector v=100i or 100kmph in the north direction, then we can talk about its acceleration.

How does acceleration take place?

Acceleration of a body can take place in three different ways:
  • By the change of speed
  • By the change of direction
  • By the change of both speed and direction
  • In any of the above cases, a body is said to be under acceleration.

How to calculate acceleration?

You can calculate acceleration in the following ways:
  • Using velocities and time intervals
    To calculate acceleration in this method, you need to know the change in velocities in a given time interval. Assuming that Vi and Vf are the initial and final velocities of a body during a certain time ‘t1’ and ‘t2’ seconds, then the acceleration ‘a’ of the body for that time interval is given by (Vf- Vi)/(t1- t2). In other words, acceleration a = Δv ÷ Δt This equation implies that the unit of acceleration is (m/s)/s = m/s2
  • Using values of force and mass
    According to Newton’s law, a body experiences acceleration based on the force acting on it. The relation between the force F acting on a body of mass ‘m’ and the resultant acceleration ‘a’ produced in it is given by F = m x a.  Thus, acceleration ‘a’ = F / m
  • Using velocity vector
    If you differentiate the velocity vector with respect to time, you will obtain acceleration. Assuming that the displacement vector is ‘s’ and velocity vector is ‘v, the acceleration a can be calculated as:

Acceleration Formula

Mass: The quantity of matter in a body; its inertia or resistance to acceleration.
– Stephen Hawking.

Terms related to Acceleration

  • Positive acceleration: A body experiences positive acceleration when the final velocity of the body is more than the initial velocity.
  • Negative acceleration: A body experiences negative acceleration when the final velocity of the body is less than the initial velocity. It is often termed as deceleration, though the appropriate term according to scientists is negative acceleration.
  • Centripetal acceleration: This is the acceleration a body experiences when it is moving in a circular motion. Here the concept of circular velocity needs to be accounted while calculating centripetal acceleration.
  • Linear acceleration: This is the acceleration when a body is moving in a straight path without changing its direction.
  • Instantaneous acceleration: This is the acceleration experienced by the body at that given instant of time or over an infinitesimally small time interval. 
  • Acceleration due to gravity: This is the acceleration that every freely falling body acquires on the Earth and is denoted by ‘g’. This is due to the gravitational force of Earth. The value of acceleration due to gravity is 9.8 m/s2

An interesting fact about acceleration due to gravity:

When two bodies of different masses are dropped from the same height, both of them experience the same acceleration due to gravity and they will touch the ground at the same time if we ignore air resistance.

Quick Question

Acceleration is a time derivative of velocity. What is the time derivative of acceleration? 

Well, the time derivative of acceleration is called Jerk, denoted by J.

Daily life examples of Acceleration

  • A freely falling body, such as a stone or an apple dropped from a certain height
  • A car speeding up while trying to overtake another car.
  • A person diving into a pool
  • A golf ball that is hit

The essential fact about acceleration

An increasing acceleration is fatal beyond a certain limit. For example, a car or a bike moving with a high level of acceleration is dangerous for travelers traveling in it. The infamous car crash of Princess Diana is an example of how high acceleration can be fatal.


It is always suggested to wear helmets and seat belts while traveling on bikes and in cars to avoid risks of accelerating speeds.

How CalculatorHut’s acceleration calculator helps you?

Acceleration calculation is essential for solving many problems in Physics. CalculatorHut’s online free acceleration calculator will help you in calculating acceleration easily.

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God can speed things up. Believe in acceleration in your life.

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