Calculus Problem

Question

A stone is thrown vertically upward from the ground at a speed of 40 m/s at time t = 0. Its distance d
(in m) above the ground (neglecting air resistance) is approximated by the function f(t) = –5t².
Determine an appropriate domain of the function. Identify the independent and dependent
variables.

Answer 1

Time is the independent variable, and distance is the dependent variable. Since time is typically not thought of as a quantity that can be negative the domain should be from [0, 8], where the square bracket represents and inclusive value, meaning it can exist at t=0 and t=8 is the final value where the function exists prior to it becoming 0. 

 

Answer 2

the independent variable is t = time

the dependent variable is distant

the domain is [0, 8] since the stone rises and falls to ground in 8 seconds

 

the actual function is d = 40t -5t² where d ranges from 0 to 80 m back to 0m