Suppose the position of an object moving horizontally after t seconds is given by the following functions s = f(t), where s is measured in feet, with s > 0 corresponding to positions right of the origin.

a. Graph the position function.

b. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left?

c. Determine the velocity and acceleration of the object at t = 1.

d. Determine the acceleration of the object when its velocity is zero.

e. On what intervals is the speed increasing?

f(t) = t² - 4t; 0 ≤ t ≤ 5