Question

Given a position function for an object, under which of these conditions is the object’s speed decreasing?

A.
when the velocity is negative and decreasing

B.
when the velocity is positive and increasing

C.
when the velocity is negative and the acceleration is negative

D.
when the velocity is negative and the acceleration is positive

E.
when the velocity is negative and the acceleration is zero

Answer 1

as a matter of differentiation, that is Calculus I, hmmmm well, the rate of any phenomena can be either positive or negative, for this case dx/dt can be either, and is only negative when the rate is decreasing.

So by definition for the position equation of s(t) when ds/dt is negative, is decreasing, keeping in mind that ds/dt is simply the derivative or rate of s(t) and is also the velocity of the object.