Determining the speed of a rocket car

[Solidearth]

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
v^o=0m/s
t_o=0s
t_f=9.0s
x_o=0m
x_f=unknown
a=unknown
v_frocket=unknown

car+parachute
v_o=unknown
v_f=unknown
x_o=x_frocket
x_fchute=990m
a_chute=-5.0m/s²
t_i=9s
t_f=12s

okay but now what, there are too many unknown variables, where would i even start?

 

[willem2]

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