Question

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.

I don't get this in word problem form

Answer 1

what's the derivative of the given s(t) with respect to t?

Answer 2

s(t) represents the distance in terms of variable t.
instantaneous velocity ( velocity ) is - as we know - is the rate of change of distance .
In math terms - rate of change is given by derivative.
so we need to have derivative of s(t) to have velocity.
instantaneous velocity is the velocity at a particular instant , here he's asking for velocity at t = 1 :)

Answer 3

find the derivative of s(t).
substitute t = 1 in the result and there you will have answer to the question.

Answer 4

so do you just plug in 1 for x? I'm confused since there's no exponent

Answer 5

I just dont get how to find the derivative since theres no exponent because I only knew how to do the power rule

Answer 6

when its given \[x^2\] you know its exponent is 2 right?
that's how when it's just x. you consider it \[x^1\] -> exponent is 1. :)

Answer 7

OH IM DUMB, thank you! Let me do this real quick

Answer 8

no problem, it happens at times :)

Answer 9

Okay, so since it's 1, nothing really changes, right? I got -17 as the answer but I know thats wrong.

Answer 10

derivative of constant is 0. FYI

Answer 11

Ugh, I'm really sorry but I don't understand that.. Could you explain?

Answer 12

do you know this definition:
\[\lim_{h \rightarrow 0}\frac{s(t+h)-s(t)}{h}=s'(t)\]

Answer 13

I don't know how to use it, no

Answer 14

actually you have a line just fine the slope of your line

Answer 15

what is the slope of s(t)=-9t-8?

Answer 16

for example the slope of y=mx+b is m
so the slope of y=-9x-8 is ?

Answer 17

hmm, derivative with respect to t means how equation changes with respect to variable t.
so when we say \[t^1\]
now for t= 1 -> we have t^1 values = 1
for t =2 -> we havr t^1 values = 2
for t =3 -> we have t^1 values = 3
so change is 2-1 = 3-2 = 1{ constant value }

Answer 18

-9

Answer 19

that is your answer

Answer 20

derivative=slope

Answer 21

really?? That's all it is?

Answer 22

yep

Answer 23

@SandeepReddy , oh I understand now!

Answer 24

Thank you both so much!!!(:

Answer 25

pleasure is ours :)