Question

a bird is flying due east, it distance from a tall building is given by x(t) = 28m +(12.4m/s)t + (0.045 m/s^3)t^3. what is the instantaneous velocity of the bird at t = 8s

Answer 1

The instantaneous velocity is how the position is changing with respect to time in a specific point in time, as opposed to the average value given by Delta(x)/Delta(t). It's given by taking a limit of Delta(x)/Delta(t) where t approaches 0, that is, by derivating x(t) in respect to t.

v(t) = x'(t) = (28 + 12.4t + 0.045t^3)' = 12.4 + 0.135t^2

But we want to find the velocity at t = 8s:

v(8) = 12.4 + 0.135*(8)^2 = 21.04m/s