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What Is The Formula For Velocity In Physics

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What Is The Formula For Velocity

Calculate Average Velocity

Far be it for us to criticize speeding tickets as a public safety tool , but maybe law enforcement officials should think about renaming them “velocity tickets.”

Allow us to make our case. You see, while the two concepts are related, the words “speed” and “velocity” do not, however, in physics, refer to the same thing.

Derivation Of Escape Velocity

The escape velocity formula can be derived in the following manner:

Let a mass be launched from the surface of the planet with a velocity equal to u. It travels to a height of h. According to the law of conservation of energy we get,

\_ = _\)

Since the potential energy of an object on the surface of the Earth is given by the formula \. This potential energy comes due to the gravitational pull of the earth and is negative because the work is done by the gravitational force of attraction.

If the initial total energy is always more than zero, then the right hand side of the above equation is always greater than zero. Thus at the height h, the body will have non-zero velocity.

\ as \

Since the escape velocity is the minimum velocity with which the projectile needs to be launched, thus the escape velocity equals to \

Instantaneous Velocity And Instantaneous Speed

When defining speed and velocity, it is also important to understand the concepts of instantaneous velocity and instantaneous speed. Instantaneous velocity and instantaneous speed both are defined as the speed of an object at a specific moment in time. However, the definition of instantaneous velocity also includes the object’s direction. To better understand this, let us consider an example of a track runner. A track runner running a 1000m race will have changes in their speed at specific moments in time throughout the entire race. These changes might be most noticeable toward the end of the race, the last 100 m, when runners begin to increase their speed to cross the finish line first. At this particular point, we could calculate the instantaneous speed and instantaneous velocity of the runner and these values would probably be higher than the runner’s calculated speed and velocity over the entire 1000m race.

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What Is The Si Unit Of Speed

SpeedvelocityunitsSI unitSI unitSI unit of speedvelocityThe Types of Velocity

  • Constant Velocity. An object with a constant velocity does not change in speed or direction.
  • Changing Velocity. Objects with changing velocity exhibit a change in speed or direction over a period of time.
  • Mathematics of Acceleration.

Solved Example On Velocity Formula

Kinematic Equation To Find Initial Velocity

Now lets test the equation with the help of examples.

Example 1- Suppose there is an object traveled a distance of 10 meters in the left direction and the time taken by the object is 2 minutes. Find the velocity of the object.


Now recall the formula which is velocity = displacement ÷ time

v = a / t

Now put the values in the formula. But first of all change minutes into time by multiplying minutes by 60.

Time in seconds = time in minutes × number of seconds in a minute

ts = 2 × 60 = 120 s

So, time in seconds is 120 s

v = 10 / 120

v = 0.08 m/s

The velocity of the object is 0.08 m/s.

Example 2- Now lets discuss another problem where we know the value of velocity and time and we have to calculate displacement. The value of velocity and time is 1.5 m/s and time taken is 100 seconds. Find the value of displacement.


Now recall the formula which is velocity = displacement ÷ time

v = a / t

Now put the value in the formula

v = a or a / t

1.5 = a ÷ 100

a = 1.5 × 100 = 150 m

The displacement is 150 m.

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The Formula For Tangential Velocity

First, we have to calculate the angular displacement \, which is the ratio of the length of the arc s that an object traces on this circle to its radius r. We measure it in radians.

The rate of change of the objects angular displacement is its angular velocity. It is denoted by \ and its standard unit is radians per second. It is different from the linear velocity, as it only deals with objects moving in a circular motion. Therefore, it measures the rate at which angular displacement is swept.

  • Tangential Velocity Formula is: \
  • Tangential Velocity Formula can also be: \
  • Another formula for Tangential Velocity is: \
  • Where,

    \ Angular Displacement

    Tangential velocity formula is applicable in calculating the tangential velocity of any object moving in a circular path. Its unit is meter per second.

    Understand Velocity Before Your Next Exam

    Understanding a variety of formulas in physics, as well as being able to distinguish the difference between velocity and speed, can help set you up for success in physics.

    If you are finding yourself struggling in physics or would like to improve your physics grade, A Team Tuition is here to help. Our tried and true tutoring methods can help you improve in any subject with at-home and online tutoring. Find a tutor near you today!

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    Example: Find Time Given Final Velocity Initial Velocity And Acceleration

    A car approaching a school zone slows down from 27 m/s to 9 m/s with constant acceleration -2 m/s2.

    How much time is required to slow down to final velocity?

    Answer: We know initial velocity , velocity and acceleration

    We first need to solve the velocity equation for time :

    v = u + at

    Plugging in the known values we get, t = /a t = / -2 m/s2 t = -18 m/s / -2 m/s2 t = 9 s

    Faqs On Velocity Formula

    Relative Velocity – Basic Introduction

    1. What is the Formula for Velocity?

    Velocity is known to be a vector quantity that measures displacement over the change in time , represented by the equation Velocity Formula = s/t. Speed is a scalar quantity that measures the distance travelled over the change in time , represented by the equation r = d/t. To find the speed, you divide the distance by the time it takes to travel that distance, and then add your direction to it. For example, if you travel 50 miles 1 hour west, your speed will be 50 miles / 1 hour west, or 50 mph west.

    2. What is the Unit of Velocity?

    Velocity is a physical vector quantity both magnitude and direction are needed to define it. It is measured in the SI as meters per second or as the SI base unit of . Velocity is defined as the distance travelled by the body during a unit somewhere. The SI unit velocity is m/s.

    3. Can Initial Velocity be Zero?

    When a body starts from rest or it changes its direction of motion, it is called initial velocity. Considering initial velocity is equal to zero , only when the object starts from rest. Generally, at the time , the initial velocity is zero. Yes, you can have zero velocity and medium velocity that is not zero. Each time when a circular motion is there in a body the movement is zero as well as its speed. An object with zero velocity has zero velocity only if it maintains a zero speed for a certain time. If not, it is faster.

    4. What makes the velocity change?

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    Initial And Final Velocity

    Initial velocity describes how fast an object travels when gravity first applies force on the object. On the other hand, the final velocity is a vector quantity that measures the speed and direction of a moving body after it has reached its maximum acceleration.

    How to find the final velocity?

    Finding the final velocity is simple with a few calculations and basic conceptual knowledge.

  • Determine the objects original velocity by dividing the time it took for the object to travel a given distance by the total distance. In the equation V = d/t, V is the velocity, d is the distance and t is the time.
  • Determine the objects acceleration by dividing the objects mass by the force and multiply the answer by the time it took for it to accelerate. For example, if the object weighs 30 kg and has a force of 15 N applied to it, then the acceleration would be 4 m/s.
  • Add the quantity obtained from Step 1 and Step 2 to obtain the final velocity. For example, if your initial velocity was 3 m/s and your object acceleration is 4 m/s, your final velocity is 7 m/s .
  • Speed Velocity And Acceleration

    Speed, velocity, and acceleration are all related to each other, though they represent different measurements. Be careful not to confuse these values with each other.

    • Speed, according to its technical definition, is a scalar quantity that indicates the rate of motion distance per time. Its units are length and time. Put another way, speed is a measure of distance traveled over a certain amount of time. Speed is often described simply as the distance traveled per unit of time. It is how fast an object is moving.
    • Velocity is a vector quantity that indicates displacement, time, and direction. Unlike speed, velocity measures displacement, a vector quantity indicating the difference between an object’s final and initial positions. Speed measures distance, a scalar quantity that measures the total length of an object’s path.
    • Acceleration is defined as a vector quantity that indicates the rate of change of velocity. It has dimensions of length and time over time. Acceleration is often referred to as “speeding up”, but it really measures changes in velocity. Acceleration can be experienced every day in a vehicle. You step on the accelerator and the car speeds up, increasing its velocity.

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    Velocity In Physics: Speed In Science

    It can be challenging to determine what type of velocity to calculate for. Be sure to ask yourself âwhat information is the equation providing?â and âwhat value am I trying to solve for?â.

    To understand physics, it is crucial that you understand the different types of velocity and how to successfully calculate them.

    Relation Between Drift Velocity And Current Density

    Physics Equation For Terminal Velocity

    We can define current density as the total amount of current passing through a unit cross-sectional conductor in unit time. From drift velocity, we know the formula for drift velocity as:I = nAvQ

    • J is the current density measured in Amperes per square meter
    • v is the drift velocity of the electrons

    Thun, we can say that the drift velocity of the electrons and their current density are directly proportional to each other. Also, when the electric field intensity increases, the drift velocity increases and the current flowing through the conductor also increases.

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    Escape Velocity Solved Examples

    Example 1: Find the escape velocity on a planet which is twice the size of the Earth.

    Solution 1: Since the escape velocity on Earth is equal to \.

    Since the planet has a size twice that of Earth thus it has a radius of 2R.

    Thus, the escape velocity would be \

    Which is equal to \

    Hope this article about the derivation of escape velocity was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the Testbook app and start browsing to get insights on them which can clear all your concepts regarding them.

    Kinematic Equations From Integral Calculus

    Lets begin with a particle with an acceleration a is a known function of time. Since the time derivative of the velocity function is acceleration,

    we can take the indefinite integral of both sides, finding

    where C1 is a constant of integration. Since \int \fracvdt=v , the velocity is given by

    Similarly, the time derivative of the position function is the velocity function,

    Thus, we can use the same mathematical manipulations we just used and find

    where C2 is a second constant of integration.

    We can derive the kinematic equations for a constant acceleration using these integrals. With a = a a constant, and doing the integration in , we find

    If the initial velocity is v = v0, then

    Then, C1 = v0 and

    which is . Substituting this expression into gives

    Doing the integration, we find

    If x = x0, we have

    so, C2 = x0. Substituting back into the equation for x, we finally have

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    Solved Examples On Instantaneous Velocity

    Q.1: Find out the Instantaneous Velocity of a particle traveling along a straight line for time 3 seconds, with a position function x defined as 5² + 2t + 4?


    As given in the function,

    x = 5t² + 2t + 4

    Differentiating the given function with respect to t, we compute Instantaneous Velocity as follows:

    Substituting function x,

    Put value of t= 3, we get the instantaneous velocity as,

    Thus the instantaneous velocity for the above function is \.

    Velocity Formula Equation In Physics For Class : Faqs

    07 – What is Instantaneous Velocity?, Part 1 (Instantaneous Velocity Formula & Definition)

    Q. What is the definition of Velocity?

    Velocity is the rate of change in displacement with respect to time. it is a measurement of how long it takes an object to travel in a straight line to its destination.

    Q. Velocity is a scalar or a vector quantity?

    Velocity is a vector quantity because it has magnitude and direction.

    Q. What is the formula of velocity?

    The formula of velocity is displacement per time.

    Q. What is the unit of velocity?

    The unit of velocity is meter/second.

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    What Is Drift Velocity

    Subatomic particles like electrons move in random directions all the time. When electrons are subjected to an electric field they do move randomly, but they slowly drift in one direction, in the direction of the electric field applied. The net velocity at which these electrons drift is known as drift velocity.

    Drift velocity can be defined as:

    The average velocity attained by charged particles, in a material due to an electric field.

    The SI unit of drift velocity is m/s. It is also measured in m2/.

    Average drift velocity and the direction of the electric field

    Velocity Formula Physics For Class 9 11

    Lets have a look at the velocity formula. As previously stated, velocity is defined as a change in an objects displacement over time. Simply said, velocity is a measurement of how long it takes an object to go in a specific direction. Furthermore, it is proportional to the displacement and inversely proportional to travel time. Its unit is also the meter per second . The formula of velocity is given below:

    We know that s = r ,v = r /t

    Now we replace /t by .

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    Quantities That Are Dependent On Velocity

    The kinetic energy of a moving object is dependent on its velocity and is given by the equation

    , }=}}=},}

    where G is the gravitational constant and g is the gravitational acceleration. The escape velocity from Earth’s surface is about 11 200 m/s, and is irrespective of the direction of the object. This makes “escape velocity” somewhat of a misnomer, as the more correct term would be “escape speed”: any object attaining a velocity of that magnitude, irrespective of atmosphere, will leave the vicinity of the base body as long as it doesn’t intersect with something in its path.

    Formula For Speed And Velocity

    Spice of Lyfe: Basic Physics Formulas Speed Distance Time

    Physics Formulas

    Speed : It is defined as the rate of change of distance, with respect to time.

    It is a scalar quantity.

    Its S.I. unit is m/s and dimensions is

    • Instantaneous speed of a particle is speed at a particular instant of time. S is the distance travelled by a particle in a time interval t, then instantaneous speed is the limiting value of S/t as t approaches zero.

    In calculus notation, this limit is called the derivative of s with respect to time, written as ds/dt

    Instantaneous speed = ds/dt.

    • Average Speed: The average speed of a particle is defined as ratio of total distance travelled to the total time taken

    If a particle travels distances S1, S2, S3.etc in time t1, t2, t3etc, respectively.

    • If a partial travels equal interval of distance of speeds v1, v2, respectively, then

    Average speed is harmonic mean of individual speeds.

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    Equations: The Speed Of A Falling Object

    Dennis -As an object falls, its speed increases because its being pulled on by gravity. The acceleration of gravity near the earth is g = -9.81 m/s^2. To find out somethings speed after a certain amount of time, you just multiply the acceleration of gravity by the amount of time since it was let go of. So you get: velocity = -9.81 m/s^2 * time, or V = gt. The negative sign just means that the object is moving downwards. If it were positive, then it would be moving up. For speed rather than velocity, you just drop the negative sign.If you have an initial velocity , then you have to include this in the equation, too, giving you: V = Vo + gt, where Vo is the initial velocity of the object. This equation will still work if you threw the ball to the side, instead of straight up or down, except that it will only give you the up-down velocity, not the total velocity. -Tamara

    What Is Escape Velocity

    Escape velocity is defined as the velocity required by an object to escape the attractive force of the Earths gravitational pull. It is the velocity that the object has to be launched and maintained during its flight until it is outside the Earths atmosphere. The escape velocity of any object depends upon the planet on which the object is, because the gravitational force depends upon the size of the planet. Thus, the escape velocity of objects also depends upon the size of the planets.

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