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

2 answers

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?
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).