Solving for Acceleration and Speed of a Rocket in Motion | Kinematics Problem

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The discussion revolves around solving a kinematics problem involving a rocket that accelerates for 16 seconds and then continues upward for an additional 4 seconds, reaching a height of 5100 meters. The initial equation derived is 5100 - x = 0.5a*16^2, where 'a' represents the acceleration during the first 16 seconds. The user initially struggles with the algebra but later clarifies that the total time of 20 seconds includes the 4 seconds after acceleration stops. They successfully formulate a system of equations to find the acceleration and speed of the rocket as it passes through the cloud at 5100 meters. Ultimately, the user resolves their confusion and outlines the steps needed to substitute values and solve for the acceleration.
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So this problem is giving me some issues, my algebra may be rusty so it has me stumped.

A Rocket experiences constant acceleration upward for 16s and then stops accelerating. It continues upward and at time 20s the distance from the ground is 5100 meters. Find the acceleration experienced during the 16s. What is the rockets speed as it passes a cloud at 5100m.


The best I could do was get the equation 5100-x = .5a*162

Where a is the acceleration during the 16s and 5100-x is equal to the distance traveled during that time.

all this coming from the basic equation Sf=S0+V0t+.5at2

This leads me to think i should use a system of equations to solve it but I am really stumped as how to begin


Any suggestions would be helpful, I'd really like to solve it on my own though so no solutions please
 
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Time 20 second is from the beginning or after 16 seconds?
 
rl.bhat said:
Time 20 second is from the beginning or after 16 seconds?

from the beginning so 4 seconds after the rocket stops
 
Nevermind, figured it out
 
If x is the distance traveled in 4 seconds, then
x = vf*4 - 0.5*g*16...(1)
vf = vi + 16*a...(2) Here vi = 0.
So x = 64*a - 8*g...(3)
You have already written
5100 - x = 0.5*a*16^2...(4)
Substitute the value of x and solve for a.
 
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