Find the derivative help please!

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.

Answer 1

So you've probably learned that velocity(V) is the derivative of position(S) with respect to time(t),

The initial equation you gave for position is S(t) = -9t - 8,

This is a linear equation, meaning that it has a constant change.

The derivative of a linear equation is always constant.

ex. for y = ax + b, the resulting derivative with respect to x is y' = a.

Therefore, V(t) = S'(t) = -9 with respect to t.

This means that the velocity at every point is -9.