Question

Explain and find the instantaneous velocity for s(t) = -3 - 7t when t = 5 seconds using the limit of the difference quotient.

Answer 1

-7 m/s

Explanation:

The limit of the difference quotient is used to find the slope passing through two point. It is gotten by taking the limit as h approaches zero. It is given by:

`(f(x+h)-f(x))/(h)`

Given that:

The function s(t) = -3 - 7t

`s(t+h)=-3-7(t+h)=-2-7t-7h`.

Using the limit of the difference quotient formula:

`Limit\ of\ difference= \lim_(h \to 0) (s(t+h)-s(t))/(h)=\lim_(h \to 0)(-3-7t-7h-(-3-7t))/(h)= \lim_(h \to 0)(-3-7t-7h+3+7t))/(h)`

`Limit\ of\ difference= \lim_(h \to 0)(-7h)/(h)= -7.\\Therefore\ instantaneous\ velocity=-7\\at\ t=5\\instantaneous\ velocity=-7\ m/s`