Determining the speed of a rocket car

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SUMMARY

The discussion focuses on calculating the speed of a rocket car that accelerates for 9 seconds before deploying a parachute that decelerates it at 5 m/s². The car travels a total distance of 990 meters in 12 seconds. To solve for the unknown acceleration of the rocket, participants suggest using kinematics equations to break the motion into two segments: the rocket phase and the parachute phase. The key is to determine the acceleration during the rocket burn to ensure the car reaches the specified distance within the given time frame.

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Homework Statement


Your school science club has devised a special event for homecoming. You've attached a rocket to the rear of a small car that has been decorated in the blue-and-gold school colors. The rocket provides a constant acceleration for 9s. As the rocket shuts off, a parachute opens and slows the car at a rate of 5m/s^2. The car passes the judges' box in the center of the grandstand, 990m from the starting line, exactly 12s after you fire the rocket.

Homework Equations


Kinematics equations


The Attempt at a Solution


by splitting the car's motion into two segments (car+rocket, and car+parachute) the motion is easier to discuss.
car+rocket
vo=0m/s
to=0s
tf=9.0s
xo=0m
xf=unknown
a=unknown
vfrocket=unknown

car+parachute
vo=unknown
vf=unknown
xo=xfrocket
xfchute=990m
achute=-5.0m/s2
ti=9s
tf=12s

okay but now what, there are too many unknown variables, where would i even start?
 
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The only unknown is the acceleration while the rocket burns. Once you know that, you know the initial location and velocity, and the acceleration at all times, so you should be able to determine the location of the car for every t.

Just set this acceleration equal to a, and find out what a must be to make x = 990 as t = 12
 

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