# diffrentiate help s(t) = 200t - 4tsquared

• Jan 15th 2013, 10:40 AM
ronanbrowne88
diffrentiate help s(t) = 200t - 4tsquared
Need hep with a problem , im not very good at calculus but ive taken a stab probly wrongly at most of them
.
As soon as it touchesdown , an airoplane applies its brakes. The distance s which the plane travles has travelled alon the runway at any subsequent time t is given by s(t) = 200t - 4t2

1) find distance travelled after 10 seconds

so do i just sub in 10 every tine ther is t i.e. 200(10) - 4(10)squared?

2)the planes speed at any time t?

do i just diffreenciate to
200 - 8t ?

3)the speed fo the plane at t=10s
i sub 10 into above formula for t?

4)the planes speed as it touches down

5)the time at which the plane comes to rest

plane come to rest when t = 0 ???

6)the distance the plane has travelled along the runway when it stops

again no idea on this one
• Jan 15th 2013, 10:52 AM
MarkFL
Re: diffrentiate help s(t) = 200t - 4tsquared
1.) Yes, find \$\displaystyle s(10)\$.

2.) Yes, \$\displaystyle v(t)=s'(t)\$.

3.) Yes, find \$\displaystyle v(10)\$.

4.) Find \$\displaystyle v(0)\$.

5.) Solve \$\displaystyle v(t)=0\$ for \$\displaystyle t\$.

6.) Use the time \$\displaystyle t=t_f\$ from part 5.) and find \$\displaystyle s(t_f)\$.
• Jan 15th 2013, 11:05 AM
ronanbrowne88
Re: diffrentiate help s(t) = 200t - 4tsquared
great thanks for clearing that up,
got them all except last one cant seeem to figure it out
, t=t_f ? not framilar with that, what is the f stand for?
• Jan 15th 2013, 11:12 AM
MarkFL
Re: diffrentiate help s(t) = 200t - 4tsquared
I just used a subscript of f on t to denote the "final" time, i.e., the time at which the plane has come to a stop.