Use the position function s(t) = –4.9t^2 + 800, which gives the height (in meters) of an object that has fallen for t seconds from a height of 800 meters
The velocity at time t = a seconds is given by the following.

lim |s(a) - s(t)
t->a | a - t

Any help would be gladly appreciated.
Thanks

Ignore the |'s, its just to separate the limit from the equation
Answer is rounded to two decimal places in M / S
Would like an explanation towards how to work it out.

This post was edited by FiestaBeast on Sep 1 2013 12:19am

do you have an actual question? i assume you wanna find velocity for some specific a?

This post was edited by carteblanche on Sep 1 2013 12:42am

haha, wow i'm an idiot.
At what velocity will the object impact the ground?

Velocity function is simply the derivative function of the position function :

v(t) = s'(t) = -9.8t

Notice that -9.8 (meters per second per second) describes the acceleration of a freely falling corpse at the surface of Earth.

You can get the velocity function step by step with your given definition (which is simply the definition of the derivative function) :
( s(a) - s(t) ) / ( a - t)
= ( -4.9a² - 800 + 4.9t² + 800 ) / ( a - t )
= ( -4.9a² + 4.9t² ) / ( a - t )
= -4.9 * ( a² - t² ) / ( a - t )
= -4.9 * ( a + t )

since a² - t² = ( a - t )*( a + t )

hence v(a) = limit ( -4.9 * ( a+t ) ) when t->a, which is -4.9 * 2a = -9.8 * a

Now you whant to know the velocity on impact. First, ask yourself at what instant t will the corpse meet the ground :
s(t) = 0 when -4.9t² + 800 = 0
solve for t.

Then plug this t into the velocity function to get your answer.

Pm if still need help !

This post was edited by feanur on Sep 1 2013 04:10am