Velocity Calculator

Introduction

Velocity is the rate of change of displacement with respect to time. It describes how fast a particle moves in space. It is a vector quantity, meaning it has both magnitude and direction defined distinctly. Our Velocity calculator will help you calculate the object’s velocity based on position and time values.

We generally measure velocity in meters/second (m/s), the standard unit.

How to use the Velocity Calculator?

Using the velocity calculator, you can calculate the particle’s velocity by inputting the required values for the formulas shown below.

Calculate Velocity using Displacement & Time

We can calculate the average velocity by dividing the change in displacement by the change in time.

The variables in the velocity calculator include

Final Position The final position of the particle or object

Initial Position The initial position of the particle or object

Time The time it takes for a particle to go from its initial to its final position.

Velocity We can calculate the velocity of the particle or object by using the following formula.

\text{Velocity} = \dfrac{\Delta x}{\Delta t} = \normalsize \dfrac{x_2 - x_1}{t_2 - t_1}

Calculate Velocity under Constant Acceleration

We can calculate the final velocity of the particle under constant acceleration.

The variables in the velocity calculator include

Initial Velocity (v0) The velocity of the particle at t0

Acceleration (a) The constant acceleration of the particle.

Time (t) The time interval for which the particle experiences constant acceleration.

Final Velocity (vt) The final velocity of the particle at the time (t) under constant acceleration. We can use the following formula to calculate it

v_t = v_0 + a*t

Calculate Velocity under Constant Acceleration using Position

we can calculate the velocity of the particle under constant acceleration given the position of the particle.

The variables in the calculator include

Initial Velocity (v0) The velocity of the particle at t0

Acceleration (a) The constant acceleration of the particle

Initial position (p0) The initial position of the particle at time t0

Final Position (pt) The position of the particle at time t

Final Velocity (vt) The final velocity of the particle at the time (t) under constant acceleration. We can use the following formula to calculate it

v_t^2 = v_0^2 + 2a(p_t - p_0)

What is Velocity?

Velocity is the rate of change of displacement with respect to change in time.

It is easy to confuse speed and velocity, and speed is a scalar quantity; it has only magnitude and no direction. Conversely, velocity is a vector quantity; it has both its magnitude and direction defined. Velocity describes how an object moves in space, how fast, and in what direction.

In physics, velocity plays a crucial role in understanding the motion of objects. It also has its role in everyday life, and we can calculate the speed of vehicles and the time it takes to get to places, the speed of a ball that a pitcher throws, or the velocity of wind, which is used to predict the intensity of storms and hurricanes.

How is Velocity Calculated?

We can calculate the velocity of an object in three ways, as shown below.

Calculate Velocity using Displacement & Time

Velocity can be calculated by dividing the change in displacement by the change in time. As shown in the following formula.

\text{Velocity} = \dfrac{\Delta x}{\Delta t} = \normalsize \dfrac{x_2 - x_1}{t_2 - t_1}

Where,

x2 → position of the particle at time t2

x1 → position of the particle at time t1

t2 → time instant, t2

t1 → time instant, t1

Calculate Velocity under Constant Acceleration

This type of motion is the simplest kind of accelerated motion wherein the object moves in a straight line under constant acceleration. The change in velocity is constant throughout, and because it is constant, we can easily calculate the final velocity of the particle by using the following formula.

v_t = v_0 + a*t

Where,

v0 → velocity of the particle at time instant t0

a → the constant acceleration of the particle during the time interval, t

t → time interval under consideration

Note: this formula is valid only for constant acceleration

Calculate Velocity under Constant Acceleration using Position

We can also calculate the final velocity of the particle given the initial position and the final position of the particle by using the following formula

v_t^2 = v_0^2 + 2a(p_t - p_0)

Where,

v0 → velocity of the particle at time instant t0

a → the constant acceleration of the particle

pt → the final position of the particle at time t

p0 → the initial position of the particle at time t0

Note: this formula is valid only for constant acceleration

Examples

Example 1

A stationary car travels to a position 2 km away in 100 seconds. What is the velocity of the car?

We can calculate the velocity of the car using the following formula

\begin{aligned} \text{Velocity} &= \dfrac{\Delta x}{\Delta t} = \normalsize \dfrac{x_2 - x_1}{t_2 - t_1} \\[10pt] &= \normalsize \dfrac{2000 - 0}{100 - 0} \\[10pt] &= 20 \; m/s \end{aligned}

The velocity of the car is 20 meters/second

Example 2

A particle is at rest at the time (t0) and is now subjected to a constant acceleration of 5 meters/second square for 5 seconds. What is the final velocity of the particle?

We can calculate the final velocity of the particle by using the following formula

\begin{aligned} v_t &= 0 + 5\; m/s^2 * 5s \\[10pt] &= 25 \; m/s \end{aligned}

The Final Velocity of the particle is 25 meters/second

Example 3

An object is at rest at time t0 and subjected to a constant acceleration of 8 meters/second square for 10 seconds. The object traveled a distance of 100 meters. What is the final velocity of the object?

We can calculate the final velocity of the particle by using the following formula

\begin{aligned} v_t^2 &= 0^2 + 2*(8\;m/s^2)(100m - 0) \\[10pt] v_t^2&= 1600 \\[10pt] v_t &= 40 \; m/s \end{aligned}

The final velocity of the object is 40 meters/second.

FAQ

Why is velocity a vector and speed is not a vector?

Velocity is given by displacement divided by time.

\text{Velocity} = \dfrac{\text{Displacement}}{\text{Time}}

Displacement is the difference between the initial and final positions of the particle. It is a vector quantity. It has direction and magnitude specified distinctly, and hence Velocity is a vector quantity.

Speed, on the other hand, we can define it as distance divided by time

\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}

Distance is a scalar quantity. It does not have any direction associated with it; hence, Speed is also a scalar quantity.

Are velocity and momentum the same thing?

Velocity and Momentum are not the same things. Velocity measures how fast the object travels, and Momentum measures mass in motion and is equal to mass times the object’s velocity. Hence, velocity and mass are used to calculate momentum.

Can velocity be negative?

Velocity is a vector quantity, and it has both magnitude and direction. Suppose the particle is moving in the positive direction of the coordinate system. In that case, the velocity will be positive if the particle moves in the opposite direction, and then the velocity will be negative.

Speed is a scalar quantity and can only be positive.

What factors does velocity depend on?

Velocity depends on two factors the displacement of the particle and the time taken.

What are the types of velocity?

The types of velocity are uniform velocity and non-uniform or variable velocity.

Uniform velocity is where the magnitude and direction of velocity remain unchanged.

If the magnitude or direction of velocity changes, it is known as non-uniform velocity.

Does velocity change with direction?

Velocity is a vector quantity dependent on the magnitude and the direction. When either the magnitude or direction changes, the velocity also changes.

What is increasing velocity called?

Any change in velocity is called acceleration. Increasing speed is called acceleration, and decreasing speed is called negative acceleration or deceleration.

What is the unit of velocity?

Velocity is usually expressed in meters per second (m/s), the SI unit. It is also expressed in other units like miles per hour, kilometers per hour (kph), kilometers per second (km/s), and feet per second.