Generally, the net force acting on an object depends on the weight of the object. The weight gives the mass times the acceleration of the object. By knowing the weight, how to find velocity with acceleration and mass?

**A certain amount of force is needed to exert on the object to cause the motion. As the object is under motion, the physical entity, velocity, acceleration, distance, and time is essential to describe its motion. All the objects possess a certain mass. Then knowing the mass and acceleration, how to find velocity is discussed.**

Mass and acceleration are the physical entity that describes the amount of force required by the body under motion. Velocity is the term that always ensures the body is in motion; we can relate these three by considering the time taken by the body travel.

**The mass of the body does not alter the velocity as the mass is a constant entity, but a body under motion possesses kinetic energy. The kinetic energy is proportional to both velocity and mass. Thus we can relate the mass and velocity. As the change in velocity gives the acceleration, we can achieve velocity from mass and acceleration.**

**How to find velocity with acceleration and mass when time is given?**

If an object is moving with acceleration a, and it has the mass m, then how to find velocity with acceleration and mass of the object is given?

**Kinematic study always describes the motion of the object in a plane. Generally, acceleration distance and time are the entity that helps to find the velocity. But** **let us try to answer the question considering the time along with mass and acceleration.**

For any object, if it is moving means some work must be done on the object. The work done on the object can be written as

W = force * total distance traveled by the object

W = F*x

We can calculate the force by using the formula F = ma.

Since the object is traveling, the total work done by the object is equal to

W = kinetic energy + potential energy

The object possesses zero potential energy because all the potential energy is lost due to the object’s motion. Hence the equation of total work done can be written as,

W = 1/2 mv^{2}

Comparing the above two equations obtained are equal.

F.x = 1/2 mv^{2}

Rearranging the terms, we get velocity as a function of force, distance, and mass.

v^{2}=2Fx/m

From the definition of velocity and acceleration, the distance traveled by the body x can be written in terms of acceleration as,

x = at^{2}

Substituting the value of distance in the velocity equation,

v^{2}=2Fat^{2}/m

Taking the square root, we get the required equation which gives the solution for how to find velocity with acceleration and distance as

v=√2Fat^{2}/m

**How to find velocity with acceleration and mass if the distance is given?**

Every object possesses certain amount of potential energy which is responsible for the object to cause motion. The potential energy turns itself into kinetic energy as the object begins to move.

**The potential energy is always associated with the mass and the acceleration of the object. There must be some work required to be done on the object to overcome the potential energy.**

The work done is given by

W = F.d

The force is given by Newton’s second law of motion as, F=ma

Therefore, the work done is W= mad

This work done is nothing but the potential energy. Once the object is overcome from the potential energy, the object begins to move with a certain velocity. Thus the kinetic energy is possessed by the same object. It can be given as

KE = 1/2 mv^{2}

The velocity of the object can be written by rearranging the terms as

v^{2} = 2KE/m

But we are unaware of the kinetic energy possessed by the body. From the law of conservation of energy, it is clear that KE = PE; when the object begins to move, the potential energy will be equal to kinetic energy. So, the equation will be

v^{2} = 2PE/m

v=√2PE/m

We are given with acceleration and mass of the object, and the distance is given; hence we can substitute the calculated value of potential energy to get the velocity.

**Example Problems on how to find velocity with acceleration and mass**

**Problem 1) An object of mass 2 kg is moving in a ramp, and for every 2 seconds, the object begins to accelerate at 3 m/s**^{2}. Calculate the velocity of the object in the ramp.

^{2}. Calculate the velocity of the object in the ramp.

**Solution:**

Given data – mass of the object m = 2 kg

Acceleration a = 3 m/s^{2}.

Time taken to accelerate t = 2 seconds.

The force applied to keep the object in motion is given by

F = ma

F = 2*3

F = 3 N.

The velocity of the object is

v=2PE*m*2Fat^{2}/m

v=√2*6*3* 2^{2}/2

v = 72 m/s.

**Problem 2) Calculate the velocity of the shot put of mass 3 kg, which is moving on a surface when the force of 23 N is applied to it and covers the distance of 6 meters.**

**Solution:**

Given data -Mass of the shot put m = 3 kg.

Force applied F = 23 N.

Distance x = 6 m.

Considering Newton’s second law, the acceleration can be given as

F = ma

a = 7.66 m/s^{2}.

From the kinematic equations, the velocity is given as

x = at^{2}

t^{2} = x/a

t = √x/a

t = 6/7.66

t=0.78 sec

v=√2Fat^{2}/m

v=√2*7,66*23*0.78^{2}/2

v= 8.45

**Problem 3) An object of mass 6 kg is sliding on a flat surface. The distance covered by the object is 12 m. The acceleration of the object is 3 m/s**^{2}. Calculate the velocity of the object and hence find the total work done on the object.

^{2}. Calculate the velocity of the object and hence find the total work done on the object.

**Solution:**

Data given – mass of the object = 6 kg.

Acceleration of the object is a = 3 m/s^{2}.

Distance covered by the object x = 12 m.

Since we have been provided with mass, distance, and acceleration, the potential energy of the object is

PE = mad

PE = 6* 3* 12

PE = 216 J.

Then the velocity of the object is

v^{2} = 2PE/m

v^{2} = 2*216/6

v^{2 }= 72

v = 8.48 m/s.

The total work done is expressed as

W = KE + PE

Since we have assumed that kinetic energy is equal to potential energy, then total work done will be

W = 2PE

W = 2* 216

W = 432 J.

**Problem 4) The potential energy possessed by the body is 116J, and the mass of the body is 4 kg. When the body starts begins to move, its potential energy is changed into kinetic energy. The distance traveled by the body is 14m. Calculate the velocity of the body and also hence find the acceleration of the body.**

**Solution:**

Data provided for the calculation

Mass of the body m = 4 kg

Distance traveled by the body d = 14 m.

The potential energy of the body PE = 116 J.

From the energy conservation laws, PE = KE. Therefore the kinetic energy is given by

KE = 1/2 mv^{2}

The velocity of the body is

v^{2} = 2KE/m

v^{2} = 2*116/4

v = 7.61 m/s.

We know that potential energy PE = mad

a=PE/md

a=116/4*14

a = 2.07 m/s^{2}.

**Problem 5) A disc of mass 2 kg is sliding on a flat surface and covers a distance of 6 meters in a time interval of 3 seconds. The acceleration of the disc is given by 4m/s**^{2}. Calculate the velocity of the disc and also find the kinetic energy of the disc.

^{2}. Calculate the velocity of the disc and also find the kinetic energy of the disc.

**Solution:**

Given – the mass of the disc m = 2 kg.

Distance covered by the disc d = 6 m.

Time taken to cover 6 m distance t = 3 s.

Acceleration of the disc a = 4 m/s^{2}. To calculate the velocity of the disc, consider the equation,

v^{2}=2Fat^{2}/m

But the force is given by the equation, F = ma

v^{2}=2(ma)at^{2}/m

v^{2} = 2a^{2}t^{2}

Substituting the given values in the above formula,

v^{2} = 2(3)^{2}(4)^{2}

v^{2} = 288

v = 16.97 m/s.

KE=1/2 mv^{2}

KE=1/2 (2*16.97^{2})

KE = 287.98 J.

**Problem 6) some amount of force is exerted on an object to begin the motion; as the force of 87 N is applied, the body begins accelerated with the acceleration of 5 m/s**^{2}. The body attains the change in the velocity of the object is given by 16 m/s. Calculate the time taken to accelerate, distance traveled by the body, and hence find the mass and the kinetic energy.

^{2}. The body attains the change in the velocity of the object is given by 16 m/s. Calculate the time taken to accelerate, distance traveled by the body, and hence find the mass and the kinetic energy.

**Solution:**

Given –Velocity of the object v = 16 m/s.

Acceleration of the object a = 5 m/s^{2}.

Force applied to the object F = 87 N.

We know that time taken by the object is given by the ratio of velocity and acceleration.

t=v/a

t=16/5

t = 3.2 seconds.

Distance traveled by the body can be calculated as

d = v*t

d = 16 *3.2

d = 51.2 m.

To find the mass of the object, let us consider Newton’s second law F = ma

m=F/a

m=87/5

m = 17.4 kg.

KE = 1/2 mv^{2}

KE = 1/2 (17.4*16^{2})

KE = 2.22*10^{3}