Use a(t) =−32 feet per second squared as the acceleration due to gravity. a ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. for how many seconds will the ball be going upward?

Since the ball is moving by uniformly accelerated motion, its vertical velocity at time t is given by

where we took upward as positive direction, and where  is the initial velocity, a the acceleration and t the time.

The instant at which is the instant when the ball reverses its velocity (from upward to downward). This means that the difference between the time t at which v(t)=0 and the instant t=0 is the total time during which the ball was going upward:

By plugging numbers into the equation, we find