Question

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

Answer 1

If we differentiate the distance function with respect to t, we get a function for velocity v(t). Sub t=2 into that for your answer.

Answer 2

so it will be s(2)=-2-6(2)=-14 ?

Answer 3

No s(t) is the distance function. Differentiate it to get a function for velocity THEN sub in t=2.

Answer 4

i dont know how to diffrentiate :(

Answer 5

At all or just for this question? The question mentions finding the derivative, are you behind in your class or something?

Answer 6

Is this from Pre-Calculus?

Answer 7

Yes it's one of my extra credit questions

Answer 8

Are you familiar with this?

Answer 9

yes!

Answer 10

Go ahead and do that. :) Btw, that equation is the long method. And I can show you the shortcut if you want.

Answer 11

Im listening

Answer 12

I suggest that you do the equation above first since it's in your lesson. Let me know if already have the answer. :)

Answer 13

wait, i am sort of confused how to plug this in

Answer 14

\[f'(t)=\frac{ f(t+h)-f(t) }{ h }\]

original equation: f(t)= -2-6t
just add the h: f(t+h)= -2-6(t+h)

Answer 15

Now substitute it to the equation.

Answer 16

i plugged it in and ended up getting -4-12t

Answer 17

Show me your work, so that I can tell where you got it wrong. :)

Answer 18

-2-6t-6h-2-6t=
-4-12t-6h=
-4-12t-6h/h=
-4-12t-6= -10-12t

Answer 19

@mathway

Answer 20

Use parenthesis. :)

\(\huge f'(t)=\frac{ (-2-6t-6h)-(-2-6t) }{ h }\)

Answer 21

is the answer -2?

Answer 22

No.

Answer 23

howwww

Answer 24

i just worked it out

Answer 25

Just distribute the negative sign!

Answer 26

oh its -6

Answer 27

Yes!

Answer 28

THANKYOUUU

Answer 29

No problem! :)

Answer 30

For the shortcut.

-2-6t

A constant's derivative is always 0! So the derivative of -2 is 0.
In -6t, notice that the exponent of the variable (in our case,t), is 1. Now, multiply the exponent to -6. Then subtract -1 from the exponent. The exponent of t is 1. So 1-1=0. Basically, the derivative of -2-6t is just -6. :)

Answer 31

Wow! that is so simple :D @mathway