A ball is thrown straight up into the air from a height of 5 feet and at an initial speed of 20 feet/second. Let s(t) denote the vertical position of the ball (measured in feet), v(t) denote the velocity of the ball (measured in feet/second), and a(t) denote the acceleration of the ball (measured in feet/second2). From physics, we know that s′(t) = v(t) and v′(t) = a(t). The careful reader will notice you have also been given s(0) and v(0) already for this particular situation. If you are told that the ball’s acceleration is given by a(t) = −16, find an equation for the po- sition of the ball (that is, find s(t)). (Hint: you are finding a particular solution of a differential equation with two initial conditions, provided above)