SOLUTION: a plane's distance in meters is described by the function s(t)=220t-15t^2-60In(t+1). 1)Find a function that describes the speed of the plane 2)Find the value of time when the s

Algebra ->  Functions -> SOLUTION: a plane's distance in meters is described by the function s(t)=220t-15t^2-60In(t+1). 1)Find a function that describes the speed of the plane 2)Find the value of time when the s      Log On


   

Question 971156: a plane's distance in meters is described by the function s(t)=220t-15t^2-60In(t+1).
1)Find a function that describes the speed of the plane
2)Find the value of time when the speed is 100ms^-1
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Speed is given as time derivative of distance
i.e. speed=+d%28s%29%2Fd%28t%29
So, speed+=+d%28220t-15t%5E2-60In%28t%2B1%29%29%2Fd%28t%29
= 220+-2%2A15t+-+60%2F%28t%2B1%29
= 220+-+30t+-+60%2F%28t%2B1%29 Ans to part 1
For part2, when speed is 100ms^-1,
220+-+30t+-+60%2F%28t%2B1%29+=+100
30t+%2B+60%2F%28t%2B1%29=+120
30t%5E2+%2B+30t+%2B+60+=+120t+%2B+120
30t%5E2+-+90t+-+60+=+0
t%5E2-3t-2+=+0
+t+=+%283%2B-+sqrt%2817%29%29%2F2
t=3.56 seconds ignoring negative value of t.