A rock thrown vertically upward from the surface of the moon at a velocity of 24m/sec reaches a height of s(t)=24t-0.8t^2 meters in t seconds.
a. find the rocks velocity and acceleration at time t
b.how long does it take the rock to reach its hihest point
c. how high does the rock go?
d. how long does it take he rock to first reach its maximum height?
e. how long is the rock aloft?

Question

A rock thrown vertically upward from the surface of the moon at a velocity of 24m/sec reaches a height of s(t)=24t-0.8t^2 meters in t seconds. 
a. find the rocks velocity and acceleration at time t
b.how long does it take the rock to reach its hihest point
c. how high does the rock go?
d. how long does it take he rock to first reach its maximum height?
e. how long is the rock aloft?

anonymous · Answer

A.
ds/dt = v (velocity)
dv/dt = a (acceleration)

B-E. This is a quadratic function, Therefore use stuff from Algebra II/Precalc to solve.
B. This is an upside down Parabola with the x coordinate of vertex at -b/2a. A=24 and b=-0.8
C. Now plug this X value into the formula and you will get the y value (height)
D is the Same question a B?????
Since it started at the ground the total time will be twice the time it took to to reach maximum height.