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

1. ## 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
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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

2. ## Re: diffrentiate help s(t) = 200t - 4tsquared

1.) Yes, find $s(10)$.

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

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

4.) Find $v(0)$.

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

6.) Use the time $t=t_f$ from part 5.) and find $s(t_f)$.

3. ## 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?

4. ## 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.