# Speed and Distance: Calculating Impact Velocity

• HellRaiser30
In summary, the conversation discusses the concept of objects colliding and the resulting change in speed and distance. The main question is if there is a formula or equation that can be used to calculate the speed of the second object based on the speed and distance of the first object after the collision. The answer is that there are several equations that can be used, depending on the specific scenario and factors such as conservation of energy and momentum, as well as the presence of dissipative forces. Examples and resources are provided for further reference.
HellRaiser30
I got a problem and it is that i have an object traveling at a certain rate of speed then another object traveling at another rate of speed hits it from behind to make the first object travel at a higher rate of speed and travel a certain distance from where it was hit till coming to a stop. If i know the distance the first object travelled, after being hit until it came to a stop, and how fast the first object was traveling at, before it got hit, is there an equation that will tell me how fast the second object must have had to been traveling at to hit the first object that distance?

One also asked:
There is one object at rest, then another object traveling at an unknown speed hits the first object causing it to accelerate to a certain speed and travel a certain distence until it comes to rest again, how do i find the unknown speed of the object that did the hitting if i know the speed that the first object accelerated to and the distance it moved.

Then what if the exact same thing happened but the object that was at rest and gets hit was already moving when it got hit and then comes to a rest.

is there a formula that i can use to find this out?
Well one has to have N equations for N unknowns. In physics, there are the laws of conservation of energy and conservation of momentum. But one must determine if the collisions are elastic or inelastic, and whether or not dissipative forces such as air-resistance or surface-to-surface friction are involved.

Please refer to these examples - http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html
http://hyperphysics.phy-astr.gsu.edu/hbase/inecol3.html

Yes, there is an equation that can help you calculate the speed of the second object. This is known as the conservation of momentum equation, which states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the momentum of the first object before the collision would be equal to the momentum of the first object after the collision, plus the momentum of the second object after the collision.

To solve for the speed of the second object, we can rearrange the equation to be:

m1v1 = m1v1' + m2v2'

Where m1 is the mass of the first object, v1 is its initial velocity, v1' is its final velocity after the collision, m2 is the mass of the second object, and v2' is the final velocity of the second object after the collision.

Since we know the initial velocity of the first object (v1), its final velocity (v1') and the distance it traveled (d), we can use the equation v1' = √(v1^2 + 2ad) to solve for v1'.

Then, we can plug this value into the conservation of momentum equation and solve for v2':

m1v1 = m1√(v1^2 + 2ad) + m2v2'

v2' = (m1v1 - m1√(v1^2 + 2ad)) / m2

This will give us the speed of the second object (v2') needed to hit the first object and make it travel a certain distance (d).

## What is impact velocity?

Impact velocity is the speed at which an object makes contact with another object or surface.

## How is impact velocity calculated?

Impact velocity is calculated by dividing the distance traveled by the time it took to travel that distance. This can be represented by the formula: v = d/t, where v is the impact velocity, d is the distance, and t is the time.

## What units are used to measure impact velocity?

Impact velocity is typically measured in meters per second (m/s), but can also be measured in other units such as feet per second (ft/s) or kilometers per hour (km/h).

## What factors affect impact velocity?

The factors that affect impact velocity include the initial speed of the object, the distance traveled, and any external forces acting on the object such as gravity or air resistance.

## Why is calculating impact velocity important?

Calculating impact velocity is important in many fields such as engineering, physics, and forensics. It helps us understand the force and energy involved in collisions, which can inform safety measures, design structures, and determine the cause of accidents.

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