How To Find Final Velocity: With Force, Mass, Time, Distance, Momentum etc And Problems


Here in this article, we will discuss how to find final velocity with acceleration and distance and how momentum and force impact on it. 

We calculate final velocity of an object by using different equations containing force, mass, time, distance and momentum. For each variable we can use different equation for finding final velocity. 

For example, to find final velocity using momentum of an object, one can use equation of momentum that isP= mv where m is mass of object, P is momentum of object and v is velocity of object.

This equation contains velocity, momentum and mass, so it can help in calculation of final velocity when mass and momentum is known. Similarly, if mass is given without momentum, then we can use mathematical form of newton’s second law of motion that is F= ma, where m is mass of the object, F is fore working on object and a is acceleration of object. Lastly for time and distance part, kinematic equations of motions are best tools for finding velocity of anybody or object.

how to find final velocity with acceleration and distance
Image credit: Snappy goat
Force, momentum, acceleration and velocity graph

How to find final velocity with force, mass and time?

As I mentioned that mathematical form of newton’s second law of motion for finding final velocity using force, mass and time. Mathematical form of second law of motion is F= ma, where m is mass of the object, F is fore working on object and a is acceleration of object. 

The equation contains force, mass and acceleration directly. 

As we know that acceleration is “rate of change of velocity with respect to time.”

So, from this formula we can find velocity when mass, force and time is known. If a body is travelling with a variable velocity, which entails a variation in velocity and/or direction, the change is considered to be in this motion.

Newton’s second law of motion, which implies how force produces adjustments in motion, addresses this movement. Newton’s second law of motion illustrates the numerical link among force, mass, and acceleration and is employed to quantify what occurs in scenarios including forces and motion. The second law is most commonly stated numerically as F= ma

How to find final velocity with distance and time?

By using first, second and third equations of motion.

First kinematic equation that is v=u+at is combination of final velocity, initial velocity, acceleration, distance and time. It will depend on particular case that which equation is to be used. Sometimes more than one equations can be used.  

In order to find final velocity when initial velocity and distance is known, third equation of motion that is v2=u2+2as can be used. And if time is given with distance and we need final velocity to calculate, then firstly we can find out initial velocity by using second equation of motion that is s=ut+1/2 at2 and then by using third equation of motion that is v2 = u2+2as, we can calculate final velocity of object. 

Computing a starting and ending velocity is a part of several physics, formulations and equations. In models for the conservation of momentum or laws of motion, the gap between starting and ending velocity tells you the velocity of an item prior and afterwards, anything occurs. It might be a force imparted to the item, a hit, or anything else that alters the path and velocity of the object.

The appropriate equation of motion can be used to compute ending velocity for an item experiencing constant acceleration. To connect them to each other, these equations require a mix of distance, starting velocity, ending velocity, acceleration, and time.

How to find final velocity with momentum?

By using equation of momentum that is P= mv], where m is mass of object, P is momentum of object and v is velocity of object.

This equation contains mass of object and velocity of object. An expression like the above might be thought of as a question-solving technique. It is possible to determine the last variable in the formula by having the integer data of all but one of the variables in the formulae.

An expression might likewise be thought of as a phrase that explains the meaningful relationship between two variables. In an expression, two variables can be viewed of as either linearly correlated or inversely related. Both mass and velocity are directly proportional to momentum. With the velocity remaining constant, an increase in mass will lead to an increase in the amount of momentum carried by the item.

Accordingly, an increase in velocity (while keeping the mass constant) would lead to an increase in the item’s momentum. We can forecast how well a change in one variable will affect the other by considering and calculating proportionally about quantities. Momentum is a vector element that has a magnitude (mathematical amount) as well as a direction. The momentum vector usually travels in a similar path as the velocity vector.

Since momentum is a vector, adding two momentum vectors is done in the same way as adding any other two vectors. When two vectors are pointing in different directions, one is regarded as negative the other is regarded as positive. The vector character of momentum must be considered in most of the questions in this group of problems for effective solutions.

How to find final velocity after collision?

Using expression for elastic and inelastic collisions.

Momentum P that is P= mv, where m is mass of object, P is momentum of object and v is velocity of object.

By conservation of momentum,“Momentum before collision = Momentum after collision”

Expression for elastic collisions

Formula for calculating final velocity of given object

v1f=m1-m2/m1+m2 (v1)+2m1-m2/m1+m2 (v2i)

Formula for calculating final velocity of colliding object

v2f=m2-m1/m1+m2 (v1)+2m1-m2/m1+m2 (vi)

Expression for inelastic collision

m1v1+m2v2=m1v1f+m2v2f

Where m1 is the mass of object before collision, v1 is the velocity of given object before collision, m2  is the mass of colliding object before collision, v2 is the velocity of colliding object before collision and  v1fis final velocity of given object and v2f is the final velocity of colliding object. 

Elastic or inelastic collisions are possible. Both momentum and kinetic energy are conserved in elastic collisions, while kinetic energy is not conserved in inelastic crashes. Inelastic collisions occur when kinetic energy is not preserved, such as when vehicles collide. The conservation of momentum applies to inelastic collisions.

As a result, momentum before the impact equals momentum after the contact. The word “momentum” corresponds to the amount of variable that a travelling item contains. The product of mass and velocity is what it’s called. and its units are kgm/s.

One may effectively determine the velocity of the vehicle after a collision using the formula below if we know the starting mass and velocity of the vehicle and the colliding object.

When particles collide in an inelastic collision, they do not act as elastic during the colliding. This indicates that the particles do not deform elastically at the site of collision; instead, they can irreversibly deform, leading to energy dissipation during a collision. This differs from an elastic collision, in which the particles bend elastically at the site of impact, behaving like flawlessly elastic springs, absorbing and releasing an equal amount of energy.   

How to find final velocity without time?

With the help of third equation of motion. 

Third equation of motion does not contain time so it is time independent.  

Third equation of motion that is v2=u2+2asis combination of initial velocity, final velocity, acceleration and distance. So we can calculate the final velocity easily when other variables are known. And it does not need time to be Known. 

If the location of an object varies with regard to a standard location, it is considered to be in motion with regard to that standard point, whereas if it does not, it is considered to be at still with regard to that point. We generate a few classic formulae pertaining to definitions distance, displacement, speed, velocity, and acceleration of the object by the formula termed equations of motion for a good awareness or to interact with the various circumstances of rest and motion.  

How to find final velocity without acceleration? 

As we discussed before the below given formula contains initial velocity of object and colliding object before collision and mass of object and colliding object before collision and final velocity. So, from here it is easy to calculate final energy of an object without knowing its acceleration.  

Considering m1 is the mass of object before collision, v1 is the velocity of given object before collision, m2  is the mass of colliding object before collision, v2 is the velocity of colliding object before collision and  v1f is final velocity of given object and v2f is the final velocity of colliding object. 

For elastic collision;  

v1f=m1-m2/m1+m2 (v1)+2m1-m2/m1+m2 (v2i)

v2f=m2-m1/m1+m2 (v1)+2m1-m2/m1+m2 (v1i) 

For inelastic collision; 

m1v1+m2v2=m1v1f+m2v2f

If we have the original mass and velocity of the provided object and the colliding item, we can use the formula below to compute the velocity of the item following collision. 

How to find final velocity without initial velocity?

When initial velocity of an object is not mentioned then we can consider the object to be at rest initially.

So, we can calculate final velocity by different formulas such as kinematic equations by putting initial velocity zero. Also, we can find the velocity of object by numerical form of second law of motion if mass of the object is known.  Another way to find velocity is using momentum formula if mass and momentum of object is known.  

Examples 

Example 1 

Let us consider a car with mass 100 kg is moving with velocity 80 m/s. Another car of mass 120 kg is moving with velocity 100 m/s. They collide with each other. Final velocity of first car after collision is 100 m/s. What will be the final velocity of second car after collision? 

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Image credit: Snappy goat
Two cars colliding

Solution

In this situation the mass m1 that is mass of first car before collision, velocity v1 of first car before collision, mass m2 of second car before collision, velocity v2 of second car before collision and final velocity v1f of first car after collision, are known. 

Given; 

m1= 100 kg

v1= 80 m/s m2= 120 kg

v2= 100 m/s

v1f = 100 m/s

Using formula for elastic collision, we can calculate final velocity of second car after collision. 

v2f=m2-m1/m1+m2 (vf)+m1-m2/m1+m2 (vi)  

v2f=(120- 100/120+ 100)100+(120(100+20))80

v2f= (0.090) 100 + 43.6363

v2f= 52.64m/s

So the final velocity of second car after collision is v2f= 52.64m/s.

Example 2  

A car start moving with initial velocity 30m/s and covers a displacement of 5 kilometers. Car achieves acceleration of   a=10m/s2. What was be the final velocity of car and how much time it will take? 

In this example initial velocity of car, acceleration of car and displacement by car is known and final velocity of car and time taken by car is asked.  

For finding final velocity, we will use third equation of motion that is combination of initial velocity, final velocity, displacement and acceleration. 

Given; 

Initial velocity, u= 30m/s

Acceleration, a=10m/s2

Displacement, s=5000m

For finding final velocity, we will use third equation of motion that is; 

v2=u2+2as

where v is final velocity of object, u is initial velocity of object and a is acceleration of object sis displacement by object.   

Putting given values in above formula 

v2=30m/s2+2(10m2s2)(5000m)

v2= 900 m2s2+(20m/s2)(5000m)

v2= 900 m2s2+100000m2/s2

v2= 100900 m2/s2

v= 317.645 m/s

So, the final velocity of car will bev= 317.645 m/s

Now for finding time taken by the to cover given displacement, we will use first equation of motion that is v=u+at. 

Putting given values in this equation, we will get 

317.645m/s=30m/s+ 10m/s2t

317.645m/s-30m/s= 10m/s2t

287.645m/s= 10m/s2t

t=287.645m/s / 10m/s}

t=28.7 s

So, the time that car will consume to reach final point is 28.7 seconds.  

Frequently asked questions |FAQs  

Q. In terms of physics, what is momentum? 

Momentum is a two-dimensional quantity that includes both a magnitude and a direction. Because momentum has a direction, it may be used to forecast the direction and speed of movement of colliding bodies. 

Q. What role does momentum play in motion? 

When two bodies hit each other, the body having greater velocity resulting in greater momentum will transmit greater power to the body having less velocity or moving slowly. 

The body with the low starting velocity shall shift off at a greater velocity and momentum in comparison to the body with the greater velocity at starting after the collision. 

Q. What are the approaches for conserving momentum? 

The variable termed momentum that defines movement in an enclosed set of components and it never varies, according to the conservation of momentum principle; that is, “the overall momentum of a system remains constant.” 

Momentum is equivalent to the impulse necessary to carry an item to a standstill in a given amount of time when its mass is multiplied by its velocity. The overall momentum of a set of entities is equal to the sum of their distinct momenta.

However, because momentum is a vector that includes both the direction and amplitude of motion, the momenta of objects moving in opposite directions can cancel out to produce a total sum of zero. 

  

SAKSHI KM

I am Sakshi Sharma, I have completed my post-graduation in applied physics. I like to explore in different areas and article writing is one of them. In my articles, I try to present physics in most understanding manner for the readers.

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