Question

The acceleration of a certain rocket is given by ax=bt where b is positive constant, find the position and velocity at t=5.0s if Xo=0 and Vo=0 and b=3.0m/s^3?

Answer 1

I assume in ax=bt, x is a subscript and not a variable. 'a' will be used from here on.

Since initial conditions are all known, the function X(t) can be found by integrations.

b=3.0 m/s³
a(t) = bt
V(t) = ∫a(t) + C1
= (b/2)t² + C1
since V(0)=Vo=0, C1=0, therefore
V(t) = (b/2)t²

X(t) = ∫V(t) + C2
= (b/6)t³ + C2
Since X(0)=Xo=0, C2=0, therefore
X(t)=(b/6)t³

Calculate X(5).