15.3k views
4 votes
(calculus !) A stone falls from a certain height in meters such that the position function of the stone is given by f(t)= -(t-5)^2 + 18, where the time T is in seconds find the velocity of the stone after six seconds

(calculus !) A stone falls from a certain height in meters such that the position-example-1
User Rob Howard
by
8.1k points

1 Answer

0 votes

We are told that the function that describes the position of the stone is given by the function


f(t)=\text{-\lparen t-5\rparen}^2+18

recall that the velocity is the derivative of the position. So we need to calculate the derivative. Recall that the derivative of a function of the form


(x\text{ -a\rparen}^2+b

where a and b are constants, is


2(x\text{ -a\rparen}

So, applying this, we get


f^(\prime)(t)=\text{-2\lparen t-5\rparen}

we want to find the value of this new function when t=6. So we have


f^(\prime)(6)=\text{-2\lparen6 -5\rparen= -2}\cdot1=\text{ -2}

so when t=6 we have the velocity is -2 m/s. This means that option B is correct.

User Dagronlund
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories