Answer
The distance (in feet) that it travels in $t$ seconds is given by
$$
s(t)=-16t^{2}
$$
The velocityi s given by
$$
v(t)=s^{\prime}(t)=-16(2)t=-32t.
$$
The velocity at each of the following times.
(a) After 3 seconds, is given by
$$
v(3)=s^{\prime}(3)=-32(3)=-96 \quad \text{ft/sec}
$$
(b) After 5 seconds, is given by
$$
v(5)=s^{\prime}(5)=-32(5)=-160 \quad \text{ft/sec}
$$
(c) After 8 seconds, is given by
$$
v(8)=s^{\prime}(8)=-32(8)=-256 \quad \text{ft/sec}
$$
(d) the acceleration, is given by
$$
a(t)=v^{\prime}(t)=s^{\prime\prime}(t)=-32(1)=-32\quad \text{ft/sec}^{2}
$$
Work Step by Step
The distance (in feet) that it travels in $t$ seconds is given by
$$
s(t)=-16t^{2}
$$
The velocityi s given by
$$
v(t)=s^{\prime}(t)=-16(2)t=-32t.
$$
The velocity at each of the following times.
(a) After 3 seconds, is given by
$$
v(3)=s^{\prime}(3)=-32(3)=-96 \quad \text{ft/sec}
$$
(b) After 5 seconds, is given by
$$
v(5)=s^{\prime}(5)=-32(5)=-160 \quad \text{ft/sec}
$$
(c) After 8 seconds, is given by
$$
v(8)=s^{\prime}(8)=-32(8)=-256 \quad \text{ft/sec}
$$
(d) the acceleration, is given by
$$
a(t)=v^{\prime}(t)=s^{\prime\prime}(t)=-32(1)=-32\quad \text{ft/sec}^{2}
$$
