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. USING THE LIMIT FORMULA TO FIND THE DERIVATIVE

Answer 1

Ughhh...the limit formula...this should be thrown in the trash the minute you start doing derivatives :P

(-8-9(t+d)-(-8-9t))/(t+d-t)

(-8-9t-9d+8+9t)/d

-9d/d (which is -9 for any value of d as well as when d approaches zero)

-9

So the instantaneous velocity is regardless of t or delta t

Answer 2

Instantaneous velocity at t = 1 by finding the derivative is -9 units.

Explanation:

The position of an object at time t is given by s(t) = -8 - 9t

Displacement, s(t) = -8 - 9t.

We need to find the instantaneous velocity at t = 1 by finding the derivative.

We have

s'(t) = 0 - 9 = -9

s'(1) = -9

So Instantaneous velocity at t = 1 by finding the derivative is -9 units.