# In-Class Problems: Static Equilibrium Solutions ```MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.01
W01D3-1: Model Rocket Solution
A person launches a home-built model rocket straight up into the air. At t = 0 the rocket
is at rest at y = 0 with v y,0 = 0. The position of the rocket is given by
a
1
y(t) = (a0 - g)t 2 - 0 4 t 6 ;
2
30t0
0 &lt; t &lt; t0
(1.1)
where a0 is a positive constant and g is the acceleration of gravity. t0 is the time that
the fuel burns out. Find the y -components of the velocity and acceleration as a function
of time. Graph the y -component of the acceleration vs. time.
Solution: We differentiate the position function to find an expression for the velocity
v y (t) valid at all times in the interval 0 &lt; t &lt; t0 .
v y (t) =
a
dy(t)
= (a0 - g)t - 04 t 5 ;
dt
5t0
0 &lt; t &lt; t0
(1.2)
We now differentiate v y (t) to find an expression for the acceleration a y (t) valid at all
times in the interval 0 &lt; t &lt; t0 .
a y (t) =
dv y (t)
dt
= (a0 - g) -
a0
t0
4
t4;
0 &lt; t &lt; t0
(1.3)
The graph below shows a plot of a y (t) vs. t for a choice of values a0 = 40 m &times; s-2 ,
g = 10 m &times; s-2 , and t0 = 2 s .
```