# Aircraft runway question - Acceleration, Time and Final Velocity

• Molly1235
In summary: Obviously a stone...so you'd decrease the mass?Yes, that would be one way to increase the acceleration. Does that answer your question?Oh, I see. So if the mass of the plane was decreased, the acceleration would also be decreased?Yes, that would be one way to increase the acceleration.

#### Molly1235

Question:

An aircraft of total mass 1.5 x 10^5kg accelerates at maximum thrust, from rest along a runway for 25s reaching the required take off speed of 65 ms^-1.

Assume that the acceleration of the aircraft is constant. Calculate the distance traveled in this time.

My attempt:

I know s = ((u+v)/2) x t
So I did 65/2 x 25 = 812.5m but u feel like this is too simple and acceleration should be involved here because it's given me the mass of the aircraft?

Many thanks!
Molly

Your result is right. If there is no additional question, you don't need the mass of the aircraft.

I get same answer as you.

It's constant acceleration so the SUVAT equations of motions can be used...

http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations

One of those is the equation you used.

Perhaps the mass was given for another part of the question? Do they ask you to calculate the thrust?

CWatters said:
I get same answer as you.

It's constant acceleration so the SUVAT equations of motions can be used...

http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations

One of those is the equation you used.

Perhaps the mass was given for another part of the question? Do they ask you to calculate the thrust?

Well there's another that asks of the length of the runway decreases, what should be changed to enable the aircraft to meet the same take off speed? The only thing I can think of is acceleration...

mfb said:
Your result is right. If there is no additional question, you don't need the mass of the aircraft.

Ah excellent! Thank you - I just quoted someone else with the sub question...think this may have something to do with the mass...

Molly1235 said:
Well there's another that asks of the length of the runway decreases, what should be changed to enable the aircraft to meet the same take off speed? The only thing I can think of is acceleration...
Yes, and how would you change the acceleration??

Molly1235 said:
...think this may have something to do with the mass...
Yes, but what?

PhanthomJay said:
Yes, and how would you change the acceleration??

Yes, but what?

Would you have to increase the mass in order to increase the acceleration??

Molly1235 said:
Would you have to increase the mass in order to increase the acceleration??
Is it easier to push a car, or to push a small stone?
Which one has a larger mass?

Hints:

* The maximum thrust (a.k.a. force) that the engine can produce is fixed.
* The mass of the plane includes the variable mass of the passengers & baggage and fuel.
* Newtons Second law (google it)

mfb said:
Is it easier to push a car, or to push a small stone?
Which one has a larger mass?

Obviously a stone...so you'd decrease the mass? Acceleration = force/mass and force is fixed, so yeah! Smaller mass = larger acceleration! I think I understand now, thank you!

At some airports in developing countries they can't take off at maximum weight (particularly when its hot and/or the runway is at high altitude). They either have to leave some passengers & baggage behind or take less fuel to reduce weight and plan a stop somewhere to refuel.

## 1. How is acceleration calculated on an aircraft runway?

Acceleration on an aircraft runway is calculated by dividing the change in velocity by the time it takes to reach that change. This can be expressed as the formula: a = (v2 - v1) / t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time it takes to reach the final velocity.

## 2. What is the relationship between acceleration and time on an aircraft runway?

The relationship between acceleration and time on an aircraft runway is direct. This means that as acceleration increases, so does time. This can be seen in the formula: a = (v2 - v1) / t. As acceleration increases, the time it takes for the aircraft to reach the final velocity also increases.

## 3. How does the length of the runway affect the time and acceleration of an aircraft?

The length of the runway does not directly affect the time and acceleration of an aircraft. However, a longer runway may allow for a longer acceleration time, resulting in a higher final velocity. Additionally, a shorter runway may require quicker acceleration in order to reach the necessary velocity for takeoff.

## 4. What factors can impact the acceleration and time on an aircraft runway?

Several factors can impact the acceleration and time on an aircraft runway, including the weight of the aircraft, wind conditions, and the condition of the runway surface. A heavier aircraft may require more time and acceleration to reach the necessary velocity, while strong headwinds may slow down the acceleration process.

## 5. How is final velocity determined on an aircraft runway?

Final velocity on an aircraft runway is determined by the acceleration and time it takes to reach that acceleration. This can be calculated using the formula: v2 = v1 + at, where v2 is the final velocity, v1 is the initial velocity, a is acceleration, and t is time. The final velocity is the speed at which the aircraft is traveling when it reaches the end of the runway.