How To Find Velocity With Acceleration And Initial Velocity: Different Approaches, Problems, Examples

In this article, we will study in detail the different approaches of how to find velocity with acceleration and initial velocity.

We can use the equations of motion formulas to find the velocity if the acceleration and initial velocity values are known. Can use the below formulas to measure the velocity of the particle,

                                                        v = u + at

                                                        v_f = v_i + at

Where a = the value of acceleration acting on a particle

              T = time

             v, v_f = velocity or final velocity

             v_i, u = Velocity at the start of movement.

Now let us know the different approaches of how to find velocity with acceleration and initial velocity.

Different Approaches of how to find velocity with acceleration and initial velocity

There are two different approaches to finding the velocity of a particle using acceleration and initial velocity. The two approaches are given below

Method 1

The first approach is to find the velocity using the acceleration formula consisting of both time and initial velocity. The formula can be derived as shown,

                                                         a = v_f – v_i /t

                                                         v_f   = v_i + at

Method 2

The second approach of how to find velocity with acceleration and initial velocity is by using the central equation of motion.

                                                           v = u + at

                                                          v = v_o + at  (Here u = v_o )

In both the approaches the terms mean as given

             a = the value of acceleration acting on a particle

              t = time

             v, v_f = velocity or final velocity

             v_i, v_o = Velocity at the start of movement.

To study in detail these approaches let us solve some problems using the above formulas.

Problems on how to find velocity with acceleration and initial velocity

By using the acceleration and V_I we can know how to find velocity using these two terms of motion.

Problem 1

A toy plane comes to rest at 65m/s and then it starts to accelerate in the other direction of the previous motion at 1.35 m/s² for 35 seconds. Measure its final velocity?

Solution: First we have to note down the given values,

U = 65m/s = initial velocity

A = -1.35m/s² (Here we use minus symbol because a is in opposite direction)

T = 35s

By using one of the equation of motion,

V = u + at

Now substitute these values in the equation that is mentioned above

V = u + at

V = (65m/s) + (-1.35m/s²) * (35s)

V = (65m/s) + (-47.25)

V = 17.75 m/s

Therefore, the velocity at the end is -17.75m/s

Problem 2

The box is made to slide over the ground. It has an acceleration value of 2m/s² and as it reaches the destination at 3.50s. Find out its velocity?

Solution: First we have to note down the given values,

V_i = 0m/s = initial velocity

a = 2m/s²

t = 3.50s

Now substitute these values in the equation that is mentioned above

v_f = v_i + at

v_f = (0m/s) + (2m/s²)(3.50s)

v_f = 7m/s.

Therefore, the velocity at the end is 7m/s.

Problem 3

A jeep moves with a constant velocity of 11km/h and suddenly accelerates at 3.3km/h for a period of 10seconds. Measure the velocity as it reaches the required position?

Solution: First we have to note down the given values,

V_i = 11km/h = initial velocity

a = 3.3km/h

t = 10s

Now substitute these values in the equation that is mentioned above

v_f = v_i + at

v_f = (11km/h) + (3.3km/h)(10s)

v_f = 44km/h

Therefore, the velocity at the end is 44km/h.

Problem 4

 A kid runs walks across the path at 2m/s and suddenly starts to run towards another street with the acceleration value of 0.60m/s² for a period of 12seconds. What will be the velocity of the kid after going to another street?

Solution: First we have to note down the given values,

u = 2m/s = initial velocity

a = 0.60m/s²

t = 12s

Now substitute these values in the equation that is mentioned above

v = u + at

v = (2m/s) + (0.60m/s²)(12s)

v_f = 9.2m/s

Therefore, the velocity at the end is 9.2m/s.

Problem 5

A piece of the stone rolled over the path at a rate of 5m/s; suddenly, it comes across a slope and gains an acceleration of 3m/s² for a time interval of 13seconds. Now, what will be the value of velocity?

Solution: First we have to note down the given values,

u = 5m/s = initial velocity

a = 3m/s²

t = 13s

Now substitute these values in the equation that is mentioned above

v = u + at

v = (5m/s) + (3m/s²)(13s)

v_f = 44m/s

Therefore, the velocity at the end is 44m/s.

So the above problems are solved to know the detailed approach of how to find velocity with acceleration and initial velocity.

Read more: How to find velocity with acceleration and time

Examples of how to find velocity with acceleration and initial velocity

For a motion to occur, many factors such as distance-time, velocity, acceleration involves. These concepts are connected. So here are some real-life examples of final, initial velocity, and acceleration.

• Spinning wheel
• Examination
• Javelin throw
• Marathon
• Juggling a ball

Spinning wheel

The spinning of a wheel can be considered an excellent example for finding the velocity. At the very initial stage, the wheel is at rest; after the motion begins, it gains some acceleration. So here, with the help of known initial velocity(u) and acceleration, we can measure the final velocity.

Examination

Before starting any exam, you will be in a constant phase of writing. So even here, as the movement of writing begins, it gains some acceleration. As time goes on, the movement of writing increases at the end of the exam. This velocity can be measured using the formulas shown at the beginning of this post.

Javelin throw

At the beginning of throwing a javelin, it consists of zero velocity as it will be at rest. While it is thrown, it acquires some motion and gains acceleration. So, we got both acceleration and initial velocity, with the help of which we can find out the velocity.

Marathon

If there is a marathon at the beginning of it, all the athletes will rest. As the marathon begins, the athletes are in movement and gain acceleration. So, we got both acceleration and V_i, with the help of which we can find out the velocity.

Juggling a ball

A person tries to have fun by juggling the balls. So before starting it, there will be no motion of balls; it will be static. But as soon as he starts to juggle, the motion gains acceleration, and using the formula; we can measure or know the velocity.

The above insights are about the different approaches, problems, and examples of how to find velocity using acceleration and initial velocity.

Frequently Asked Questions | FAQs

What is the function of velocity, and why does it matter?

The measure of position in motion is known by velocity.

When a body moves from one position to another, it requires some velocity to move. To know how much speed you acquired to move, we use velocity. It is the crucial function of velocity, and in motion, the quantity velocity matters a lot.

What do you mean by initial velocity?

In simple terms, we can say that the beginning velocity is the initial velocity.

So to define initial velocity, one can tell that the velocity that a body gains at the very beginning of the movement or the starting velocity of the particle as soon as the motion begins is termed as initial velocity(u).

Mention the difference between initial and final velocity?

The initial and final velocities are different from each other.

The rate of the magnitude of speed a particle possesses at the very beginning of the motion is the initial velocity. The rate of the magnitude of speed a particle as soon as it reaches its destination is termed to be final velocity.