Answer to Question #148141 in Calculus for Sean

Question

A toy rocket rises vertically in such a way that t seconds after its liftoff, it is
s(t) = -16t^2 + 200t feet above the ground.
(a) How high is the rocket after 6 seconds?
(b) What is the average velocity of the rocket over the first 6 seconds of flight (between t=0 and t=6)?
(c) What is the instantaneous velocity of the rocket at t=2 sec?

Answer 1

we have general equation of distance; s(t)=-16t²+200t;

a) to find the height of the rocket after 6 seconds we need to put 6 in place of t in the equation,

s(t)=-16*6²+200*6=576-1200=-624;

b) average velocity is v_avg=s/t_total; in our case, v_avg=-624/6=-104;

c) in order to find the instantaneous velocity of the rocket we need to take the derivative of the distance function and put 2 sec in place of t; ds(t)/dt=v(t)

ds(t)/dt=-32t+200, v(2)=-64+200=136