Need help with physics airplane runway question

[booder111]

Homework Statement

length of runway for airplane 1.5miles, accelerate at 3.0m/s^2 decelerate at 2.1m/s
What length of time is available from the start of the motion to decide on a course of action (take off or abort)

Homework Equations

d=a*t 3.0m/s/-2.1m/s

The Attempt at a Solution

so far we have 804 seconds acceleration and -1149 seconds for deceleration

 

[willem2]

Homework Equations

d=a*t 3.0m/s/-2.1m/s

The airplane is accelerating, or decelerating. This is the equation for constant speed.

The Attempt at a Solution

so far we have 804 seconds acceleration and -1149 seconds for deceleration

After 804 seconds of 3 m/s^2 acceleration, the speed of the airplane will be 1206 m/s.
It will have covered 970 km

suppose the airplane is accelerating until time T. How many meters does it move?
If the airplane starts decelerating at time T, how long does it take before it stands still?
How many meters does it move in that time?
The sum of these 2 distances should be equal to the length of the runway, in the limiting case
where the airplane is just able to stop in time. This will give you an equation that you can solve
for T.

 

[tomcue]

.

Hello,

Thank you for reaching out for help with your physics homework. It seems like you are trying to solve for the time available to make a decision during the takeoff or abort process on an airplane runway. To solve this problem, we will need to use the equations of motion, specifically the one you have mentioned which is d = at. This equation represents the distance (d) traveled by an object with a constant acceleration (a) over a certain amount of time (t).

In this case, we have two different accelerations, one for the takeoff process (3.0 m/s^2) and one for the abort process (2.1 m/s^2). To find the total time available, we need to find the time for each process separately and then add them together.

Takeoff process:

We know that the distance (d) is equal to 1.5 miles, which we need to convert to meters for consistency with the given accelerations. 1.5 miles is approximately 2414 meters.

Using the equation d = at, we can solve for time (t):

2414 = (3.0)t
t = 2414/3.0 = 804 seconds

Abort process:

For the abort process, we are given a deceleration of -2.1 m/s^2, which is a negative value because the airplane is slowing down. We also know that the distance (d) is still 2414 meters.

Using the same equation, d = at, we can solve for time (t):

2414 = (-2.1)t
t = 2414/-2.1 = -1149 seconds

Note that the negative sign indicates that the time for the abort process is in the opposite direction of the takeoff process.

Total time available:

To find the total time available, we need to add the time for the takeoff process and the abort process together:

Total time = 804 + (-1149) = -345 seconds

This means that the total time available to make a decision is approximately 345 seconds. However, please note that this calculation assumes that the airplane is traveling at a constant acceleration throughout the entire process, which may not be the case in real life situations. It is always important to consider other factors and variables when making decisions in a scientific or engineering setting.

I hope this helps you with your homework. Remember to always double check your calculations and assumptions, and