Answer:
Average speed after traveling 800ft: 120 feet/sec in = 6.67 seconds*
If p(t) is the position function, that is, the jet is p(t) feet down the catapult path after t seconds, then:
p'(t) is the instantaneous speed of the jet after t seconds.
p''(t) is the acceleration of the jet, which we are given is constant. So:
[i] p''(t) = c
[ii] p'(t) = ct + k
[iii] p(t) = ½ct² + kt + K
for some constants c, k, and K.
Since we know that the jet starts from a dead stop at the beginning of the catapult run, we know that k and K are zero. So, we have:
[iii] 800 = ½ct²
....1600 = ct²
c = 1600/44.44444
c = 36
or
[ii] 240 = c(6.67) + 0
.....c = 36
