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

@ivancsc1996

Answer 1

I assume you mean \(s(t)=-1-13t\)?

If that's the case, what's the derivative? What's the value of the derivative with \(t=8\)?

Answer 2

The velocity of a particle undergoing one dimensional motion is \(v=\frac{ds}{dt}\). So we fist find the velocity as a function of time.
\[v(t)=\frac{ds}{dt}(t)=-13\]
So we find that the object is moving with constant velocity (independent of time). Therefore, the answer is -13 at all times (including \(t=8\)).