# Velocity Question: Initial vs. Final Velocity at y=0

• Miike012
In summary, the conversation discusses the relationship between initial and final velocities in a projectile motion problem. It is stated that, in the absence of external forces, the final velocity at the instant before the object collides with the ground will equal the initial velocity. This is due to the conservation of energy in the system. However, if air resistance is included, the final velocity will be less than the initial velocity. It is also noted that, in the case of a projectile, the horizontal component of velocity remains constant throughout the motion.

#### Miike012

My question is... If I have an initial velocity (V0) will the final velocity(Vf) at y = 0 be equal?

I created a diagram if the question is confusing...
If so, why is this true? Because wouldn't final velocity be zero??

#### Attachments

• velocity.png
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Essentially these types of problems are asking you the velocity at the instant before the object collides with the ground. Hence, unless there are external forces dissipating the objects energy, its final (at the instant before it touches ground) will equal its initial.

I think this is the qoestion on projectile motion. If air resisance is neglected, final velocity is equal to initial velocity. It will never become zero throughout the time of flight. if air resistance is included, final velocity will be less than initial one.

Miike012 said:
My question is... If I have an initial velocity (V0) will the final velocity(Vf) at y = 0 be equal?

I created a diagram if the question is confusing...
If so, why is this true? Because wouldn't final velocity be zero??

The velocities in the picture are not equal, but of equal magnitude, as the directions differ. You can say that the speeds are equal.

If it is a projectile, the horizontal component is constant during the motion as only vertical force -gravity- acts on the object. Energy is conserved, so mgyi+1/2 mvi2=mgyf+1/2 mvf2. If yi=yf the square of the velocities are equal, vi2=vf2. That means equal magnitudes |vi|=|vf|, that is, equal speeds.

ehild

I would like to clarify that the final velocity at y=0 will not always be equal to the initial velocity. This depends on the specific conditions and factors involved in the motion.

To understand this, we need to first define what we mean by "initial velocity" and "final velocity". Initial velocity (V0) refers to the velocity of an object at the beginning of its motion, while final velocity (Vf) refers to the velocity of the object at the end of its motion.

Now, let's consider the scenario described in the question. If an object has an initial velocity (V0) and is moving along the y-axis, the final velocity (Vf) at y=0 will be equal to the initial velocity only if there are no external forces acting on the object. In other words, if the object is moving with constant velocity in a straight line without any forces acting on it, then Vf=V0.

However, if there are external forces acting on the object, such as gravity or friction, then the final velocity (Vf) will not be equal to the initial velocity (V0) at y=0. This is because these forces can change the velocity of the object as it moves along the y-axis.

To answer the question about why final velocity is not always zero at y=0, we need to consider the concept of acceleration. When an object is moving along the y-axis, it may experience a change in velocity due to the acceleration caused by external forces. This means that the final velocity at y=0 will not be zero, as the object may still be moving with a certain velocity due to the acceleration it experienced.

In conclusion, the final velocity at y=0 will not always be equal to the initial velocity, as it depends on the presence of external forces and the acceleration experienced by the object. It is important to consider all the factors involved in order to accurately determine the final velocity at a specific point in motion.

## 1. What is the difference between initial velocity and final velocity?

The initial velocity is the velocity at the beginning of a motion or the starting point of a trajectory. The final velocity is the velocity at the end of a motion or the end point of a trajectory.

## 2. How is initial velocity calculated?

Initial velocity can be calculated using the formula v = (d/t), where v is the initial velocity, d is the distance traveled, and t is the time taken.

## 3. How is final velocity calculated?

Final velocity can be calculated using the formula v = (u + at), where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

## 4. Why is initial velocity important?

Initial velocity is important because it determines the starting point of an object's motion and can affect its final velocity and overall trajectory.

## 5. How does initial velocity affect final velocity at y=0?

At y=0, the final velocity will be equal to the initial velocity if there is no acceleration or change in direction. However, if there is acceleration or a change in direction, the final velocity will be affected by the initial velocity and other factors such as time and distance traveled.