Question

Any help with derivatives would be helpful

The position of an object at time t is given by s(t) = 1 - 10t. Find the instantaneous velocity at t = 10 by finding the derivative.

Answer 1

Do you know how to find instantaneous velocity?

Answer 2

v = s/t is the equation for velocity i know. s is displacement and t is time.

Answer 3

What grade are you in? I learned it by doing x(2)-x(1)/t(2)-t(1)

Answer 4

12th. im not the best with derivatives so that part confuses me

Answer 5

Okay. So, s(t) represents the position of the object or the distance it has travelled from its starting point at time t.
The derivative of distance is velocity. I.e., it is the change is distance divided by the change in time as in miles per hour or feet per second.

The derivative of s(t) with respect to t in this case is -10
So, your velocity is a constant -10. You can test this by calculating the position at various times like t=0, t=1, t=2, etc. Then compute the velocity at those times. Since the velocity is constant average and instantaneous velocity are the same.

Does this make sense?

Answer 6

It does a bit more. Thank you sparklyme

Answer 7

Sure!