# Solving Speed of Objects Problem

• yankees26an
In summary, the formula for calculating speed is speed = distance / time, or v = d/t. The distance traveled by an object can be found by multiplying the speed by the time it takes to travel, or d = v x t. Average speed is the total distance traveled divided by the total time taken, while instantaneous speed is the speed of the object at a specific moment in time. To convert units, you can use unit conversion factors, such as multiplying by 1000/3600 to convert from km/h to m/s. Acceleration is the rate of change of an object's speed and can cause an object to increase or decrease its speed, depending on the direction of the acceleration.
yankees26an

## Homework Statement

A bomb that is originally at rest blows apart into three pieces of equal mass. Two of the
pieces have velocities (12i + 24j) m/s and (30i - 24j) m/s. What is the speed of the third
piece?

## Homework Equations

m1v1 + m2v2 + m3v3 = 3mv4 (assuming m is the same)

## The Attempt at a Solution

Not really sure where to begin. I can find the speed of the 2 objects by finding the k direction, but that's it.

Hint: What's the total momentum of all three pieces?

As a scientist, the first step in solving this problem would be to understand the concept of conservation of momentum. This principle states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the system consists of the three pieces of the bomb.

Next, we can use the given information to set up an equation using the conservation of momentum principle. This equation would be:

m1v1 + m2v2 + m3v3 = 3mv4

where m represents the mass of each piece and v represents the velocity of each piece.

Since we know that the mass of each piece is equal, we can simplify the equation to:

v1 + v2 + v3 = 3v4

Now, we can substitute the given velocities for v1 and v2, and solve for v3:

(12i + 24j) + (30i - 24j) + v3 = 3v4

42i = 2v3

v3 = 21i

Therefore, the speed of the third piece is 21 m/s in the i direction.

In conclusion, by understanding the concept of conservation of momentum and setting up the appropriate equation, we can solve for the speed of the third piece of the bomb. This solution not only helps us find the answer to the given problem, but it also showcases the importance of understanding fundamental principles in solving scientific problems.

## 1. What is the formula for calculating speed of an object?

The formula for calculating speed is speed = distance / time, or v = d/t. This formula can be used for both average speed and instantaneous speed.

## 2. How do you find the distance traveled by an object?

The distance traveled by an object can be found by multiplying the speed by the time it takes to travel. So, distance = speed x time, or d = v x t.

## 3. What is the difference between average speed and instantaneous speed?

Average speed is the total distance traveled divided by the total time taken, whereas instantaneous speed is the speed of the object at a specific moment in time. Average speed gives an overall picture of an object's speed, while instantaneous speed gives a more specific and detailed view.

## 4. How do you convert units when solving speed problems?

To convert units, you can use unit conversion factors. For example, to convert from kilometers per hour (km/h) to meters per second (m/s), you would multiply by a conversion factor of 1000/3600, which is equivalent to dividing by 3.6. This can be applied to any unit conversion, as long as the units are equivalent.

## 5. How does acceleration affect the speed of an object?

Acceleration is the rate of change of an object's speed. If an object is accelerating, its speed will be changing over time. The greater the acceleration, the faster the object's speed will change. So, acceleration can cause an object to increase or decrease its speed, depending on the direction of the acceleration.

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