# Grade 12 Calculus plane deceleration question

speeddman

## Homework Statement

When an F-18 jet lands on the runway, it's position is defined by s(t)=189t-t^7/3 meters after t seconds

calculate the braking time

calculate the deceleration when the jet stops ( i think she means immediately before?)

derivative

## The Attempt at a Solution

s'(t)=189-7/3t^4/3

Homework Helper

## The Attempt at a Solution

s'(t)=189-7/3t^4/3

What about the derivative, you want to find a t for which s'(t) is what value?

speeddman
@rock.freak667

well i dunno wouldn't taking the derivative help me find how long it takes to stop?

Homework Helper
@rock.freak667

well i dunno wouldn't taking the derivative help me find how long it takes to stop?

Ok what does the derivative represent ?

speeddman
the derivative would represent the deceleration wouldn't it? because the function represents the time.

speeddman
***distance/time

Homework Helper
***distance/time

Which is velocity right? So if it is braking, what should the final velocity be?

speeddman
...0?

Homework Helper
...0?

Right, so what do you get for t when you equate s'(t) to zero?

speeddman
81=t^4/3

so t=0.92448s

so it takes 0.92448s for the plane to stop.

now for to find the deceleration at an instantaneous pnt i have to take second derivative?

Homework Helper

## The Attempt at a Solution

s'(t)=189-7/3t^4/3

81=t^4/3

so t=0.92448s

so it takes 0.92448s for the plane to stop.

now for to find the deceleration at an instantaneous pnt i have to take second derivative?

You have two differing statements. Check it over.

speeddman
well s'(t)=189-7/3t^4/3

0=189-7/3t^4/3

-189/(-7/3)=t^4/3

81=t^4/3

4/3root of 81= t

t=0.92448s

does that make sense?

speeddman
no it doesnt. 1.3333333333333root of 81 = 27s

Homework Helper
no it doesnt. 1.3333333333333root of 81 = 27s

Yes 27s works better.

Now how would you get the acceleration from s'(t)?

speeddman
second derivative?

s''(t)=(-28/9)t^1/3

Homework Helper
second derivative?

s''(t)=(-28/9)t^1/3

and if it takes 27 seconds to stop, what is the deceleration at that instant?

speeddman
(-84/9) m/s^2

thank you so much by the way for everything!

is that right?

speeddman
(-84/9) m/s^2

Thanks for everything by the way!

is that right?

Homework Helper
Yes that is correct.