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 - 4t^{2}

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

not sure about this

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

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 $\displaystyle s(t_f)$.

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?

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.