Math Calculators
Velocity Calculator

Velocity Calculator

Free online velocity calculator solves for v, u, a or t using velocity formula. Calculate the final velocity (v) using the equation v = u + at.

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Table of Contents

  1. The Equations of Motion
  2. The First Equation of Motion
  3. The First Equation Applications
  4. Final Velocity Calculation
  5. Initial Velocity Calculation
  6. Acceleration Calculation
  7. Time Calculation
  8. A Brief History of the First Equation of Motion
  9. Conclusion

Velocity Calculator

Imagine being able to calculate the precise speed at which an object is moving, or determining the exact moment an object will reach its final destination. These calculations may seem daunting, but with the power of a velocity calculator, they become more real.

The speed and acceleration calculator uses the formula v = u + at, where v is final speed, u is initial speed, a is acceleration, and t is travel time. It finds any unknown variable given the other three. Note, however, that the equation v = u + at assumes constant acceleration throughout the time of motion.

With the ability to calculate initial velocity as u = v - at, acceleration as a = (v - u)/t, and travel time as t = (v - u)/a, this velocity calculator becomes the ultimate tool for physics students, engineers, and anyone in need of determining the motion of an object. The user-friendly interface of the velocity solver requires only the input of known values, and it accepts a variety of imperial and metric units for input.

So, whether you're a physics student trying to understand the motion of a projectile, an engineer designing the next big machine, or a wave energy enthusiast, a velocity calculator is the tool for you.

The Equations of Motion

Equations that explain the nature and behavior of a physical system in terms of its motion are called the equations of motion. There are three equations of motion that can be used to calculate the parameters of motion, such as distance, velocity (initial and final), time (t), and acceleration (a) of an object.

Below are three equations of motion:

  • The first equation of motion: v = u + at
  • The second equation of motion: s = ut + ½ at²
  • The third equation of motion: v² = u² + 2as

Where v is final velocity, u is initial velocity, t is time, a is acceleration, s is distance traveled.

The First Equation of Motion

In physics, the equation of velocity, v = u + at, relates the final velocity of an object, its initial velocity, acceleration, and the time it takes to reach its final velocity. This equation is widely used in physics and engineering to calculate the motion of objects.

The equation has four variables: the initial velocity (u), the final velocity (v), the acceleration (a), and the amount of time (t).

  • The initial velocity is the object's velocity at the beginning of its motion.
  • Final velocity is the object's velocity at the end of its motion.
  • Acceleration is the rate at which an object's velocity changes over time.
  • Time is the duration of motion.

To explain in simple words, the first equation of motion says that an object's velocity (v) is equal to its initial velocity (u) plus the product of its acceleration (a) and the elapsed time (t). It tells us how an object's velocity changes over time due to constant acceleration.

The First Equation Applications

The equation v = u + at is a way to comprehend and forecast how different things move, like projectiles, waves, and mechanical systems.

Scientists can employ this equation to study the behavior of projectiles. In the broadest sense, a projectile is an object that is thrown, shot, or projected into the air. Naturally, the motion of such objects obeys the laws of physics.

Applying the first equation of motion, we can compute the trajectory of a projectile. To accomplish this, we must take into account factors such as initial velocity, projection angle, and air resistance. For example, knowing the initial velocity and launch angle, we can predict where the projectile will land, whether it is a baseball or a rocket.

The first equation of motion is employed in mechanical engineering. Engineers employ this equation to design and analyze the motion of machines such as cars, airplanes, and robots. They utilize it to compute the velocity and acceleration of moving parts, such as pistons in an engine, which allows them to design more efficient and powerful engines.

The equation of motion we're discussing in this article pertains to the study of waves. In more general terms, waves are disturbances propagating in space. And their motion can be described mathematically using the first equation of motion.

By comprehending the velocity and acceleration of waves, scientists and engineers can forecast the behavior of waves under different conditions and design systems to harness their energy. For instance, engineers can make wave energy converters that work better by studying the speed and acceleration of ocean waves. Scientists can employ the first equation of motion to predict how sound waves will behave in different places and design systems to harness their energy.

In aerospace engineering, engineers employ the first equation of motion to compute the velocity and acceleration of airplanes and optimize their performance.

In other fields such as materials science, the first equation of motion is used to study the behavior of materials under different loading conditions, which helps to improve the design and performance of the materials. It's also used in biomechanics to study the motion of human body parts, which helps in the design of prosthetic devices and physical rehabilitation. Overall, the first equation of motion is a versatile tool that can be applied in a wide range of fields to understand and predict the motion of various systems.

Final Velocity Calculation

Let's use our multifunctional tool as a final velocity calculator. In this section we will find the final velocity of a moving object using the First Equation of Motion: v = u + at.

Consider a cyclist riding a bicycle with an initial velocity of 6 meters per second. Let us suppose that the cyclist is accelerating uniformly at a rate of 0.6 meters per second squared. The question is, what will be the cyclist's velocity after 20 seconds? Or what is the final velocity in this problem?

Substituting the given values of initial velocity (u = 6 m/s), acceleration (a = 0.6 m/s²), and time (t = 20 s) into the velocity formula, we get:

v = u + at = 6 + (0.6 × 20) = 6 + 12 = 18 m/s

Therefore, the cyclist's velocity after 20 seconds will be 18 meters per second.

Initial Velocity Calculation

Let's examine a practical example of utilizing the first equation of motion to calculate the initial velocity of an object. In this case we will use this variation of the equation: u = v – at.

Imagine that a car is traveling at a final velocity of 25 meters per second, with an acceleration of 2 meters per second squared. If we know that the car has been in motion for 10 seconds, we can use the equation v = u + at to determine the initial velocity of the car.

We can substitute the known values of final velocity (v), acceleration (a), and time (t) into the equation, or to allow the initial velocity calculator to solve in for you.

u = v - at = 25 - (2 × 10) = 25 - 20 = 5 m/s

Therefore, the initial velocity of the car in this scenario is approximately 5 meters per second.

Acceleration Calculation

To solve the problem of finding the acceleration we should rearrange the First Equation of Motion and use it as:

a = (v - u) / t

Let's find the acceleration of a vehicle by considering an example where its velocity changes from 0 km/h to 100 km/h in 2.5 seconds.

It is essential to ensure that all units are consistent before substituting the given values. In this case, we must convert the velocity from km/h to m/s.

0 km/h equals 0 m/s and 100 km/h equals 27.78 m/s.

Given the initial velocity (u) of 0 m/s, the final velocity (v) of 27.78 m/s, and the time (t) of 2.5 seconds, we can calculate acceleration as follows:

a = (v - u) / t = (27.78 - 0) / 2.5 = 27.78 / 2.5 = 11.11 m/s²

Thus, the acceleration of this car is 11.11 meters per second squared or around 11 meters per second squared.

Time Calculation

Using the formula t = (v - u)/a, you can find the time it takes for an object to reach a certain velocity or vice versa to slow down.

Imagine that the car is traveling at an initial velocity of 60 miles per hour and decelerates to a final velocity of 20 miles per hour with a constant acceleration of -2 meters per second squared. Let’s calculate the time this car needs to decelerate.

First we need to convert the velocity of the car from miles per hour to meters per second. 60 miles per hour are equal to 26.82 meters per second and 20 miles per hour are equal to 8.94 meters per second.

By entering in the equation t = (v - u)/a the initial velocity (26.82 m/s), final velocity (8.94 m/s), and acceleration (-2 m/s²) we can calculate the time.

t = (v - u) / a = (8.94 - 26.82) / -2 = -17.88 / -2 = 8.94 s

Therefore, the time this car needs to decelerate to a final velocity of 20 miles per hour is 8.94 second or around 9 seconds. This information can be valuable for safety purposes and determining the time it takes for the car to slow down on a particular stretch of road.

A Brief History of the First Equation of Motion

Aristotle is often credited as the originator of the notion of kinematics, which is the mathematical description of the motion of idealized objects. Thus, the basics of kinematics go back to ancient Greece.

However, the mathematical formulation of kinematics as we know it now began to take shape in the 17th century through the pioneering work of Galileo Galilei and Sir Isaac Newton. Both of these brilliant scientists made significant contributions to the field of kinematics and laid the foundation for modern physics.

Galileo Galilei was one of the pioneers in the field of kinematics. He was the first to experimentally demonstrate that the acceleration of an object under the influence of gravitational forces remains constant. He also showed that the velocity of an object increases uniformly with time while maintaining the same acceleration using a pendulum.

Sir Isaac Newton, who is widely regarded as the father of modern physics, expanded on Galileo's work and formulated the laws of motion. Newton's second law of motion states that the force exerted on an object is proportional to the product of that object's mass and acceleration. This relationship can be expressed mathematically as a = F/m.

The first equation of motion, v = u + at, which relates the final velocity of an object to its initial velocity, acceleration, and time, is derived from Newton's second law of motion by assuming that the total force acting on an object remains constant.

It is important to note that this equation is only valid when acceleration remains constant. In situations where acceleration is not constant, the equation becomes more complex and requires the application of more advanced mathematical calculations to find a solution.


The formula for speed v = u + at helps us better understand how things move and behave by allowing us to calculate things like final velocity, initial velocity, acceleration, and travel time.

A speed calculator can help us learn more about the world around us in many ways, including improving our understanding of the motion of cars, projectiles, and wave dynamics. The Speed Calculator is a handy and intuitive tool for anyone interested in physics, whether you are a scientist, engineer, or student.