Answer:
t = 2 s= 96
t = 3 s = 64
t = 4 s= 32
t= 5 s = 0
t= 6 s = -32
t = 7 s = -64
t = 8 s = -96
t= 9 s = -128
Step-by-step explanation:
We have the equation of the position of the rocket as a function of time t.
[tex]f(t) = -16t^2 + 160t[/tex]
The instantaneous velocity of the rocket as a function of time is given by the derivation of the position with respect to time.
So
[tex]S(t)=\frac{df(t)}{dt} = -2*16t + 160\\\\S(t) = -32t+160[/tex]
[tex]s(1) = -32(1)+160=128\ ft/s\\\\s(2) = -32(2)+160=96\ ft/s\\\\s(3) = -32(3)+160=64\ m/s\\\\s(4) = -32(4)+160=32\ m/s\\\\s(5) = -32(5)+160=0\ m/s\\\\s(6) = -32(6)+160=-32\ m/s\\\\s(7) = -32(7)+160=-64\ m/s\\\\s(8) = -32(8)+160=-96\ m/s\\\\s(9) = -32(9)+160=-128\ m/s[/tex]
So
t = 2 s= 96
t = 3 s = 64
t = 4 s= 32
t= 5 s = 0
t= 6 s = -32
t = 7 s = -64
t = 8 s = -96
t= 9 s = -128
