Final answer:
The object's velocity at time t is -32t ft/sec, speed is 32t ft/sec, and acceleration is -32 ft/sec^2.
Step-by-step explanation:
To find the object's velocity at time t, we need to first find its acceleration. The equation for the object's height above ground at time t is given by 5 = 159 - 16t^2. Taking the derivative with respect to time, we find that the acceleration is -32 ft/sec^2. The velocity is then found by integrating the acceleration with respect to time, and the initial condition is given by v(0) = 0. So the object's velocity at time t is v(t) = -32t ft/sec.
The object's speed at time t is the magnitude of its velocity, so the speed is given by |v(t)| = |-32t| = 32t ft/sec.
The object's acceleration at time t is given by a(t) = -32 ft/sec^2.