Optimizing Landing Time and Distance for a Plane with Maximum Acceleration

[chocolatelover]

Homework Statement

A plane lands with a speed of 80.0 m/s and can accelerate with a maximum magnitude of 6.00 m/s^2 as it comes to rest. From the instant the plane touches the runway, what is the minimum time interval needed before it can come to rest?

b. what is the minimum distance the plane requires to land?

Homework Equations

vxf-vxi=integral o to t axdt
vxf=vxi+axt
d=(vi+vf/2)t

The Attempt at a Solution

a. vi=80.0m/s
vf=0m/s
a=6.00 m/s^2

Is this right so far?

Would I then use the formula vxf=vxi+axt and solve for t?

b. d=(vi+vf/2)t

Now I just need to solve for d, right?

Thank you very much

 

[berkeman]

Looks right so far.

 

[chocolatelover]

Thank you very much

Does this look correct?

vi=80m/s
vf=0m/s
a=6.0m/s^2

vxf=vxi+axt

0m/s=80m/s+6m/s^2t
t=-13.333

d=vi+vf/2(t)
d=(80m/s+0m/s/2)(-13.333)
=-533.32

but this can't be correct because the time and distance are negative.

Do you see where I made my mistake?

Thank you very much

 

[berkeman]

You wrote: 0m/s=80m/s+6m/s^2t

But the "acceleration" in this case is a deceleration, so the sign on the "acceleration" term should be negative.

 

[chocolatelover]

Thank you very much

Regards