Question 10.4: Given the result of Eq. (10.43), find the relation for the b...

Equation (10.43) can be written as

Hence, integrating from time t=0 to time t, we have

                                                          \int_{0}^{t}{\left[r(t)\right]^{2} }\frac{dr}{dt}dt=\int_{0}^{t}{\frac{\overline{\nu }_{s}a^{2} }{4} }dt,
or
                                                  \frac{\left[r(t)\right]^{3} }{3}-\frac{\left[r(0)\right]^{3} }{3}=\frac{\overline{\nu }_{s}a^{2} }{4}t

and, thus,