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Acceleration Calculator

Introduction

Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction defined distinctly. The Acceleration calculator will help you calculate the acceleration based on input variables.

Any velocity change is called acceleration, and if an object speeds up or slows down, the object is accelerating.

We measure Acceleration in units like meters/second^2 or feet/second^2

How to use the Acceleration Calculator?

Using the acceleration calculator, you can calculate the acceleration of an object by inputting the required values for the formulas shown below.

Acceleration using Velocity

We can calculate the average acceleration along a direction using change in velocity and change in time. The variables in the acceleration calculator include:

Final Velocity (v2) The final velocity of the particle or object

Initial Velocity (v1) The initial velocity of the particle or object

Time (t) The time it takes for a particle to go from initial velocity to final velocity

Acceleration (A) We can calculate the acceleration of the particle by the following formula

Acceleration=ΔvΔt=v2−v1t2−t1\text{Acceleration} = \dfrac{\Delta v}{\Delta t} = \normalsize \dfrac{v_2 - v_1}{t_2 - t_1}

Acceleration using Force Applied

We can also calculate the acceleration by using the force applied to the particle or the object by using Newton’s Second Law of Motion.

Newton’s Second Law of Motion states that the acceleration of an object depends upon the mass of the object and the amount of force applied, we can write the relationship as follows.

F=m∗aF = m*a

The variables in the acceleration calculator include:

Force (F)
The magnitude of the external force applied to the object

Mass (m)
The mass of the object

Acceleration (a)
We can calculate the acceleration of the particle by using the following formula

Acceleration=ForceMass\text{Acceleration} = \normalsize \dfrac{\text{Force}}{\text{Mass}}

What is Acceleration?

When a particle is in motion along a straight line, the velocity of the particle is the rate of change of position with time, and it tells us how fast and in what direction the particle moves.

When the particle speeds up or slows down, the rate of change of velocity with time is called acceleration.

We generally use meters per second squared (m/s^2) as the unit of acceleration.

The average acceleration of a particle is given by the change in velocity divided by the time interval.

The instantaneous acceleration of a particle is defined as the acceleration of the particle at any specific instant of time.

How is Acceleration Calculated?

We can calculate Acceleration in two ways, one is using the change in velocity over the time interval. Another method is by using the force applied.

Calculate Acceleration using Velocity

The average acceleration is given by the change in the velocity divided by the time interval, as shown by the following formula

A=ΔvΔt=v2−v1t2−t1\text{A} = \dfrac{\Delta v}{\Delta t} = \normalsize \dfrac{v_2 - v_1}{t_2 - t_1}

Where,

v2 → instantaneous velocity at the instant of time t2

v1 → instantaneous velocity at the instant of time t1

t2 → time instant, t2

t1 → time instant, t1

Calculate Acceleration using Force Applied

When an external force acts on an object, it causes the object to accelerate in the same direction as the external force. This is what Newton’s second law of motion tells us. The following formula describes the relationship.

F=m∗aF = m*a

Where,

F = External Force Applied

m = mass of the object

a = acceleration that the object experiences

Mass is a scalar quantity, and so it does not have a direction component. Force is a vector quantity, so it has both magnitude and direction, and hence acceleration is a vector quantity. The direction of acceleration will be in the same direction as the force.

The magnitude of acceleration will be directly proportional to the magnitude of the external force acting on the object. If the magnitude of the external force is constant, then the magnitude of acceleration will also be constant.

The magnitude of the acceleration is inversely proportional to the object’s mass. The greater the mass of the object, the smaller the acceleration. The lesser the mass of the object, the greater the acceleration.

Acceleration using the Velocity and Time Graph

We could also find the acceleration using the velocity and time graph.

Untitled

At time t1, the particle has velocity v1 and is denoted by point x1 on the curve, and at time t2, the particle has velocity v2 and is denoted by point x2 on the curve.

As shown above, the average acceleration is the slope of the line joining the two points x1 and x2

The instantaneous velocity at a point is tangent to the curve at that point.

Examples

Example 1

Let us consider a stationary car, which accelerates to a velocity of 20 m/s over 5 seconds. What is the average acceleration of the car?

The average acceleration of the car can be calculated by using the following formula

A=v2−v1t2−t1=20−05−0=4  m/s2\begin{aligned} \text{A} &= \normalsize \dfrac{v_2 - v_1}{t_2 - t_1} \\[10pt] &=\normalsize \dfrac{20 - 0}{5 - 0} \\[10pt] &= 4 \; m/s^2 \end{aligned}

The car’s average acceleration turns out to be 4 meters / second square.

Example 2

Given a force of 50N is applied to a particle with a mass of 5kg. What is the acceleration of the particle?

The acceleration of the particle can be calculated by using the following formula

a=Fm=505=10  m/s2\begin{aligned} a &= \normalsize \dfrac{F}{m} \\[10pt] &= \normalsize \dfrac{50}{5} \\[10pt] &= 10 \; m/s^2 \end{aligned}

The acceleration of the particle is 10 meters/second square

FAQs

What is the difference between acceleration and velocity?

Velocity describes how position changes with respect to time, and acceleration describes how velocity changes with respect to time. So, if an object is increasing its velocity, then we can say it is accelerating. If the object is decreasing its velocity, then it is decelerating.

What causes acceleration?

According to Newton’s second law, acceleration results from a net force applied to an object. Hence, the acceleration produced is directly proportional to the force applied and inversely proportional to the object’s mass.

Can an object have constant acceleration?

If a particle’s velocity changes at a constant rate, then we can say that the particle is in constant acceleration. When an object is in free fall, we can say that the object will have constant or nearly constant acceleration due to gravity. The object will have an acceleration of 9.806 m/s^2

How does acceleration affect velocity?

Acceleration is the change in velocity with respect to time. Suppose the direction of acceleration is the same as velocity. In that case, the object will speed up, and if the direction of the acceleration is in the opposite direction as velocity, the object will slow down.

What is instantaneous acceleration?

Instantaneous acceleration is the rate at which the particle’s velocity changes at a given instant in time. So, using a graph of velocity and time, we can get the slope of the tangent to the velocity curve which gives the instantaneous acceleration.

What is uniform acceleration?

Acceleration that does not change in terms of magnitude and direction it’s called uniform acceleration. When an object experiences uniform acceleration, the object’s change in velocity will be constant.

How do you find the final velocity of an object, given its acceleration?

You can find the velocity of an object by using the following formula

vt=v0+a⋅tv_t = v_0 + a \cdot t

Where,

vt → final velocity of the object

v0 → initial velocity of the object

a → acceleration experienced by the object

t → the time interval during which the object experiences acceleration

How do you find the final position of an object, given its acceleration?

You can find the final position of an object given its acceleration by using the following formula

x=x0+v0t+12at2x = x_0 + v_0t + \dfrac{1}{2}at^2

Where,

x → Final position of the object

x0 → Initial position of the object

v0 → initial velocity of the object

a → acceleration experienced by the object

t → the time interval during which the object experiences acceleration

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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