Question

The acceleration of a certain rocket is given by a(t)=bt where b is positive constant compute the the average velocity of the rocket between t=4.5s and 5.5s at t=5.0s if x(t)=0 and b=3.0m/s^3, compare this average velocity and instaneous velocity at t=5.0s

Answer 1

You cannot compute the velocity from the acceleration information alone. There has to be information provided on the initial velocity or the velocity at some specific time.

The statement x(t)=0 does not make sense. It means x is always zero. At what time is x = 0?

Answer 2

If V(0)=0, you can look up the answer for:
http://www.jiskha.com/display.cgi?id=1255001673
The equations and data are the same.

The average velocity can be done by taking the difference in distance travelled between t=4.5 and t=5.5 and divide by Δt.
Vmean=(X(5.5)-X(4.5)/(5.5-4.5)

You can compare the results with the average with the actual velocity V(5).