This all-in-one online Acceleration Calculator performs calculations using three methods. All three methods are applicable to uniformly accelerated motion. The first method uses a formula that relates the acceleration of an object to its initial and final velocity and the time it has been in motion. The second method uses a formula that relates the acceleration of an object to its initial and final velocity and the distance traveled. And, finally, the third method uses the formula of Newton’s second law, which relates the acceleration of an object to its mass and the force acting on the object.
You can select a method first, then enter the values of any known parameters into the input fields of this calculator and press the ‘Calculate’ button to find the missing parameter.
What is Acceleration in Physics
Acceleration in mechanics is defined as the change in velocity per unit of time. Velocity, on the other hand, is the rate at which an object’s position changes over time. In simpler terms, acceleration measures how quickly an object’s speed or direction changes. It is a vector quantity, meaning it has both magnitude and direction.
Thus, the average acceleration of an object over a period of time can be expressed by the following general formula:
$$ \overline{\textbf{a}}=\frac{\textbf{v}_f \ – \ \textbf{v}_i}{t},$$
where
\(\overline{\textbf{a}}\) is the average acceleration,
\(\textbf{v}_i\) is the initial velocity,
\(\textbf{v}_f\) is the final velocity,
\(t\) is the elapsed time.
Acceleration has dimension L·T−2. The SI unit for acceleration is meter per second squared (m·s−2). Another popular unit is feet per second squared (ft·s−2).
Uniformly Accelerated Motion
Uniformly accelerated motion occurs when an object experiences a constant acceleration throughout its motion. This means that the object’s velocity changes by the same amount in equal time intervals. Examples of uniformly accelerated motion include an object falling freely under gravity, a car moving with constant acceleration, or a ball rolling down an inclined plane.
For simplicity, in what follows we will consider the motion of objects along a straight line, so that the velocity vector of the object and its acceleration vector are parallel.
In this case, the previous formula can be written in scalar form. In addition, instead of the average acceleration, the constant (or instantaneous) acceleration \(a\) will be used in the formula:
$$ a=\frac{v_f \ – \ v_i}{t}.$$
It is this formula that is used in the first method of calculating acceleration in our Acceleration Calculator.
Distance Traveled in Uniformly Accelerated Motion
Knowing the initial and final velocity of an object, and its acceleration, it is not difficult to find the distance traveled. But the formula obtained in this way can also be used to find the acceleration over a known distance:
$$ a=\frac{v_{f}^2 \ – \ v_{i}^2}{2d},$$
where \(d\) is the distance traveled.
We use this formula in the second method of calculating acceleration in our online calculator.
Newton’s Second Law
According to Newton’s second law of motion the acceleration vector of the body’s center of mass is proportional to the net force vector (i.e. sum of all forces) acting on it:
$$ \textbf{F}=m \textbf{a},$$
where
\(\textbf{F}\) is the net force acting on the object,
\(m\) is the mass of the object,
\(\textbf{a}\) is the center-of-mass acceleration.
We use the scalar version of this formula in our Acceleration Calculator to find acceleration using the third method.
Related calculators
Check out our other physics calculators such as Momentum Calculator or Velocity Calculator.