Question

The position of an object at time t is given by s(t) = 3 - 4t. Find the instantaneous velocity at t = 8 by finding the derivative.

Answer 1

This is a linear function so it is going to have a constant rate of change (i.e. constant velocity).

First differentiate:

s(t) = 3 - 4t

s'(t) = -4

s'(8) = -4

(The instantaneous velocity at any point will also be -4)

Insert units here if you have them. Like if the y axis says metres, and the x axis says seconds, then your answer should be -4m/s.

Hope this helps.