Rocket's Max Height: Model Rocket w/ 70.0 m/s Initial Speed

[Kildars]

A model rocket is launched straight upward with an initial speed of 70.0 m/s. It accelerates with a constant upward acceleration of 1.00 m/s2 until its engines stop at an altitude of 190 m.

(a) What is the maximum height reached by the rocket?
m

I don't know what I am doing wrong here. I have two pages full of screw ups, haha.

I tried to find out the final velocity it hits right before it runs out of fuel and I'm stuck

Using:
$$x = x_0 + v_0 t + (1/2) a t^2$$

I did 190 = 0 + (70)t + 1/2(1)(t^2)

I get down to 190 = 70t + .5t^2

I'm just lost so just some guidance would be nice, I know the steps I'm just making a simple error somewhere or something and I've tried for like 60 minutes, so I figured I'd post.

 

[blackwizard]

U don't have or need a time variable so that's the wrong equation of motion. This 1 shud work better:
$$v^2 = v_0^2 + 2ax$$

The other 1s r listed here if u need em:
http://en.wikipedia.org/wiki/Equations_of_motion

 

[Astronuc]

The rocket starts with an initial velocity 70.0 m/s and accelerates at a rate of 1 m/s² over a distance of 190 m to a greater velocity at which point it stops accelerating (because the motor cuts out = no more thrust) and it starts decelerating with gravity -9.8 m/s².

So there are two parts to the problem.

1. The acceleration phase to 190 m. So solve for a constant acceleration problem over 190 m with v_o = 70 m/s, and find the velocity at 190 m.

2. With the velocity determined in 1) determine the altitude the rocket achieves with that initial velocity at 190 m.

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1

 

[Kildars]

Thank you, I got the answers using your help.

A model rocket is launched straight upward with an initial speed of 70.0 m/s. It accelerates with a constant upward acceleration of 1.00 m/s2 until its engines stop at an altitude of 190 m.

(a) What is the maximum height reached by the rocket?
455.68 m
(b) How long after lift-off does the rocket reach its maximum height?
10.06 s
(c) How long is the rocket in the air?
19.876 s