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

Answer:

-7 m/s

Step-by-step 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:

$\frac{f(x+h)-f(x)}{h}$

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:

$Limit\ of\ difference= \lim_{h \to 0} \frac{s(t+h)-s(t)}{h}=\lim_{h \to 0}\frac{-3-7t-7h-(-3-7t)}{h}= \lim_{h \to 0}\frac{-3-7t-7h+3+7t)}{h}$

$Limit\ of\ difference= \lim_{h \to 0}\frac{-7h}{h}= -7.\\Therefore\ instantaneous\ velocity=-7\\at\ t=5\\instantaneous\ velocity=-7\ m/s$