# Do I need to consider mass in the equations?

• SavannahN
And then you can chop up the continuum into segments and calculate average acceleration for each segment.In summary, the average acceleration of a rocket can be calculated using the formula a = Δv/Δt, where a is the average acceleration, Δv is the change in velocity, and Δt is the change in time. This formula can be used to find the average acceleration from the start to t1 and between t1 and t2. The mass of the rocket does not need to be taken into account as it is already taken into consideration in the force producing the acceleration. Additionally, the "2" in the formula aavg = Δv/(2*Δt) is incorrect and should not be used.
SavannahN

## Homework Statement

a. At launch a rocket ship has a mass M. When it is launched from rest, it takes a time interval t1 to reach speed v1; at t = t2, its speed is v2.
What is the average acceleration of the rocket (i) from the start to t1 and (ii) between t1 and t2?

For now, I am taking question a as example, but these are the follow up questions:

(b. Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel (i) from the start to t1 and (ii) between t1 and t2?

c. Use your symbolic results to calculate the average accelerations and distances for M = 2.25 * 106 kg, t1 = 8.00 s, v1 = 158 km/h, t2 =1.00 min, and v2 = 1580 km/h.)

## Homework Equations

a= Δv/Δt
F = M * a?
s = vavg * Δt (in follow up questions)

## The Attempt at a Solution

a) a= Δv/Δt
-> aavg = Δv/(2*Δt)
i) aavg = v1/(2*t1)
ii) aavg = (v2-v1)/(2*(t2-t1))

Is this correct or did I need to use mass M in the equations?

1. No, you don't have to use the mass to find the average acceleration. The force is already acting on the mass to produce such acceleration, so mass is already taken into account, resulting in those change in velocities.

2. Where did you get the "2" in aavg = Δv/(2*Δt) ? Why is it there?

Please note that aavg is defined as the change in velocity over that time period, i.e. Δv/Δt. It appears that you're taking a "statistical" definition of "average" here, which may account for the appearance of the "2". This is NOT how it is defined in physics.

Zz.

ZapperZ said:
Where did you get the "2" in aavg = Δv/(2*Δt) ? Why is it there?
Oh, yes, I see I made a mistake in thinking that dividing by 2 got me the average velocity.

ZapperZ said:
It appears that you're taking a "statistical" definition of "average" here, which may account for the appearance of the "2".
The notions of average are the same in both disciplines. The distinction is between averaging over a uniformly weighted discrete distribution of two elements (sum the element values and multiply by the uniform weight of 0.5) and a time-weighted continuous distribution (e.g. integrate the acceleration over time from start to finish and divide by elapsed time from start to finish).

Of course, if you integrate acceleration over time from start to finish, you get delta v between start and finish. So you get a formula that looks different, but ultimately it is the same concept.

SavannahN

## 1. Do I need to consider mass in the equations?

Yes, mass plays a crucial role in many scientific equations and calculations. It is a fundamental property of matter and affects various physical phenomena.

## 2. How does mass affect motion?

Mass is directly related to an object's inertia, which is its resistance to changes in motion. The greater the mass, the greater the inertia, making it harder to accelerate or decelerate the object.

## 3. Can mass be converted into energy?

Yes, according to Einstein's famous equation E=mc^2, mass and energy are interchangeable. This means that mass can be converted into energy, and vice versa, under certain conditions.

## 4. How does mass affect gravitational force?

The greater an object's mass, the greater its gravitational force. This is because mass is a factor in the calculation of gravitational force, along with distance and the universal gravitational constant.

## 5. Is there a difference between mass and weight?

Yes, mass and weight are two different concepts. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Therefore, an object's mass will remain the same regardless of its location, but its weight will vary depending on the strength of gravity.

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