Constant Acceleration one dimension

1. Sep 18, 2009

Neophyte

1. The problem statement, all variables and given/known data
A rocket starting at rest takes on a net acceleration of 20m/s^2 in a vertical line until it runs out of fuel after 5 seconds.

At what height does it run out of fuel?
What is its velocity when it runs out of fuel?
What is its maximum height?
How long does it take to hit the ground?

2. Relevant equations
g = -10m/s^2

3. The attempt at a solution
x(t) = 1/2at^2 + Vot

Vo = 0
a = 20m/s^2
t = 5

a)10(25) m = 250m
b)v(t) = at + vo
v(t) = (20)(5) = 100 m/s

c) max height
v(t) = 0
at + vo = 0
at = 0
*;/

d) x(t) = 0
1/2at^2 + Vot
5t^2 + 0

What did I do wrong :/. The net acceleration part is confusing me. Is the Vo zero?

2. Sep 18, 2009

physicsface

You need to do more kinematics starting at the point when the rocket runs out of fuel. Now your only acceleration is gravity, and you've got the rocket's velocity at this point and its elevation. Find its displacement from this point of reference.

3. Sep 18, 2009

Neophyte

Hm,
So...
c)
Vo = 100m/s

v(t) = -10t + 100m/s
0
-100/-10 = t
t = 10 s
x(10) = -500 + 1000
= 500m
d) = 20 s?

4. Sep 18, 2009

physicsface

c) You forgot about the elevation it was already at! The rocket's at 500 m displacement from the reference point at 250 m, so what's the elevation at the peak?

d) You need to include the 5 seconds it takes to run out of fuel as well as the time it takes to get through the last 250 m of its fall.