Thread: free falling object

Use the position function s(t) = -16t^2 + 1000, which gives the height in feet of an object that has fallen for t seconds from a height of 1000 feet. the velocity at time t = a seconds is given by:

lim s(a) - s(t)
t to a a - t

if a construction worker drops a wrench from a height of 1000 feet, how fast will the wrench be falling after 5 seconds?

the answer is 160ft/sec
but i am not sure how to get there,
this is what i have so far:

-16 * 5^2 +1000 = 600

600 - (-16t^2 + 1000)
5 - t

where do i go from here? please help!

600 - (-16t^2 + 1000
5 - t


= (16*t^2- 400)/(5-t)

= 16(t^2-25)/(5-t)

= 16(t-5)(t+5)/(5-t)

= -16(t+5)

lim -16(t+5) =-160
t->5

This is the velocity hence the negative sign indicating it is moving down

the speed is 160