If a stone is thrown down at 100 ft/s from a height of 1,250 feet, its height after t seconds is given by s = 1,250 − 100t − 16t^2
Estimate its instantaneous velocity at time t = 2

Question

If a stone is thrown down at 100 ft/s from a height of 1,250 feet, its height after t seconds is given by s = 1,250 − 100t − 16t^2
Estimate its instantaneous velocity at time t = 2

swissgirl · Answer

We know that the equation for instantaneous velocity is 
$ f'(x)=\large \frac{f(x+h)-f(x)}{(x+h)-x}$

swissgirl · Answer

Are you familiar with this equation?

anonymous · Answer

yes

swissgirl · Answer

so $f(t)=1250-100t-16t^2$

$f(t+h)=1250-100(t+h)-16(t+h)^2$

so $f'(x)= \large \frac{(1250-100(t+h)-16(t+h)^2)-(1250-100t-16t^2)}{(x+h)-x}$

$f'(x)=\large \frac{1250-100t-100h-16t^2-32th-16h^2-1250+100t+16t^2}{h}$

$ f'(x)=\large \frac{-100h-32th-16h^2}{h}$

$f'(x)= \large \frac{h(-100-32t-16h)}{h}$

$f'(x)=(-100-32t-16h)$

swissgirl · Answer

Ok Are you familiar with limits?
Like what does f'(t) equal as h approaches 0?

swissgirl · Answer

Did ya follow so far?

anonymous · Answer

Yes I follow so far

swissgirl · Answer

Ok and keep in mind by accident I used X's in stead of T's so just ignore that

swissgirl · Answer

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