SOLUTION: A rocket of mass m = 500 kg is travelling in a straight line for a short time. The distance in metres covered by the rocket during this time is described by the function s(t) =

Question 971939: A rocket of mass m = 500 kg is travelling in a straight line for a short time.
The distance in metres covered by the rocket during this time is described
by the function
s(t) = 220t - 15t2 - 60 ln (t + 1)
where t > 0 is the time in seconds.
a.) Find a function that describes the speed of the rocket.
b.)Find a function that describes the acceleration of the rocket
c.)Find the value of time t when the speed of the rocket is 100 ms^−1
Amy.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A rocket of mass m = 500 kg is travelling in a straight line for a short time.
The distance in metres covered by the rocket during this time is described
by the function
s(t) = 220t - 15t2 - 60 ln (t + 1)
where t > 0 is the time in seconds.
a.) Find a function that describes the speed of the rocket.
Speed is the 1st derivative.
s'(t) = 220 - 30t - 60/(t+1)
-----------------
b.)Find a function that describes the acceleration of the rocket
Accel is the 2nd derivative
---------------------
s"(t) = -30 + 60/(t+1)^2
c.)Find the value of time t when the speed of the rocket is 100 m/sec
s'(t) = 220 - 30t - 60/(t+1) = 100
30t + 60/(t+1) = 120
t + 2/(t+1) = 4
t^2+t 2 = 4t+4
t^2 - 3t - 2 = 0
Solve for t, use the positive solution.
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