Help please! The position of an object at time t is given by s(t) = -4 - 2t. Find the instantaneous velocity at t = 6 by finding the derivative.

Question

anteater · Answer

Hello - So, to begin with, what would the derivative with respect to t of -4 - 2t be?

anonymous · Answer

I have had a lot of trouble with this whole module so I don't actually know.. Maybe you can help?

anteater · Answer

Ok. Your function is -4 - 2t, and the derivative of that would just be -2, since the derivative of -4 (a constant) is 0 and the derivative of -2t is -2.

anonymous · Answer

Okay I got that

anteater · Answer

So then you also know that the derivative (or slope) of the displacement, s(t), is the velocity

anteater · Answer

In other words, s'(t) = v(t)

anteater · Answer

And so here it appears the velocity is constant and is -2.

anonymous · Answer

Alright

anteater · Answer

I don't know if they have any additional questions about this problem ... for example, do they ask about acceleration?

anonymous · Answer

No, the full question is the one that I posted!

anteater · Answer

Ok :)

anteater · Answer

If you would like another way of thinking about it, this may help. They tell you that s(t), the particle's position as a function of time, is -4-2t, which is just a line with a slope of -2.

anteater · Answer

So that means that the slope (velocity) at any point along the line will be -2. Does that make more sense?

anonymous · Answer

Thank you!

anteater · Answer

You're welcome :) Do you have any other questions?