Question

Need help quickly please! The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative.

Answer 1

The derivative of a position function is the velocity function. Can you find the velocity function?

Answer 2

I have no idea how. Could you take me through it?

Answer 3

Oh man, I'm not good at teaching derivatives.

Answer 4

We can take it one term at a time.
So we need to find the derivative of f(x). We can find the derivative of each term.

Answer 5

Alright so what do i do?

Answer 6

Let's do -8 first. The derivative of a constant is ALWAYS ZERO. Aight?
We have this so far:
f(x) = -8 - 9t
f'(x) = v(t) = 0 + ____

Answer 7

ok ya that makes sence

Answer 8

I shouldn't have put that plus sign, but it's ok. We can look at -9t as one term now.

Answer 9

sense*

Answer 10

With -9t, we use the Power Rule for derivatives:
\[\frac{d}{dx}x^n = n*x^{n-1}\]

Answer 11

hmm ok how do i use it

Answer 12

Plus, we can isolate the -9 as a multiple of t, which is another property of derivatives.
It can be written as this:
-9 * t^1, right?

Answer 13

Can you apply the power rule to this term to find its derivative?

Answer 14

d/d(9) 9^n=n*9^n-1?

Answer 15

Uh no, you're apply the rule to t. I'll show you now. We also keep -9 as a multiple:
\[\frac{d}{dt} -9t = -9*\frac{d}{dt}t^1 = -9*1*t^{0} = -9 \]

Answer 16

You see how I applied the rule? The third step?

Answer 17

ya i think so... what's next

Answer 18

Well, that's the last term of the function. We write it nicely now:
f(x) = -8 - 9t
v(t) = 0 - 9 = -9

Answer 19

so the answer is -9? wow thanks so much!

Answer 20

v(t) = -9; When you plug in anything for t, what value will you get?

Answer 21

depends on the value of t?

Answer 22

The velocity function looks like a horizontal line through y-value -9.
So, at any time 't', the velocity will be -9 units

Answer 23

Yeah, it depends on the value of t. Not always will we get a constant for the velocity function.

Answer 24

oh ok, thanks so much :)