Question

The position of an object at time t is given by s(t) = -1 - 13t. Find the instantaneous velocity at t = 8 by finding the derivative.

Answer 1

start by finding the derivative of s(t) ?

Answer 2

i dont know how to find the derivative of
-1-13 because there are no exponents or anything

Answer 3

\[s(t) = -1-13t\]

whats the derivative of \(-1\) with respect to \(t\) ?

Answer 4

is it -8?

Answer 5

nope
derivative of a constant is 0

Answer 6

ohh okay, so then what would the instantaneous velocity be?

Answer 7

there is another term in s(t)

whats the derivative of \(-13t\) ?

Answer 8

if it helps notie that \(-13t\) is same as \(-13t^1\)

Answer 9

-13t^0?

Answer 10

yes! simplify

Answer 11

-13?

Answer 12

thats it!

\[s(t) = -1-13t\]
\[s'(t) = 0 - 13 = -13\]

Answer 13

thank you so much!!

Answer 14

yw!