Question 1067802
{{{0}}} feet per second is the initial velocity,
because the stone was simply let go.
{{{v(t)=0+32t}}} --> {{{highlight(v(t)=32t)}}} ,
where {{{v(t)}}} is the downwards velocity in feet per second,
and {{{t}}} is the time in seconds since.
{{{highlight(Range="[ 0 , 192 ]")}}} ,
because the stone's velocity starts as o feet per second,
and increases all the way to 192 feet per second.
The formula for {{{v(t)}}} obviously apply to the time the stone is falling,
not before it is dropped, and not after it hits the ground.
so we need to find how long it was falling, by solving
{{{192=32t}}} --> {{{t=192/32}}} --> {{{t=6}}} .
{{{highlight(Domain="[ 0 , 6 ]")}}} ,
because the formula/function {{{v(t)}}} applies only to
{{{t=0seconds}}} (time the stone is dropped),
{{{t=6seconds}}} (time the stone hits the ground),
and all the values of {{{t}}} in between.