  In this paper, we examine an inverse problem for the following convective
Brinkman-Forchheimer (CBF) equations or damped Navier-Stokes equations:
  \begin{align*}
  \boldsymbol{v}_t-\mu
\Delta\boldsymbol{v}+(\boldsymbol{v}\cdot\nabla)\boldsymbol{v}+\alpha\boldsymbol{v}+\beta|\boldsymbol{v}|^{r-1}\boldsymbol{v}+\nabla
p=\boldsymbol{F}:=\boldsymbol{f} g, \ \ \ \nabla\cdot\boldsymbol{v}=0,
  \end{align*} on a torus $\mathbb{T}^d$, $d=2,3$. The inverse problem under
consideration consists of determining the vector-valued velocity function
$\boldsymbol {v}$, the pressure gradient $\nabla p$ and the vector-valued
forcing function $\boldsymbol{f} $. Using the Tikhonov fixed point theorem, we
prove the existence of a solution for the inverse problem for 2D and 3D CBF
equations with the final overdetermination data for the divergence free initial
data in the energy space $ \mathbb{L}^2(\mathbb{T}^d)$. A concrete example is
also provided to validate the obtained result. Moreover, we overcome the
technical difficulties while proving the uniqueness and H\"older type stability
results by using the regularity results available for the direct problem for
CBF equations. The well-posedness results hold for $r \geq 1$ in two dimensions
and for $r \geq 3$ in three dimensions for appropriate values of $\alpha,\mu$
and $\beta$. The nonlinear damping term $|\boldsymbol{v}|^{r-1}\boldsymbol{v}$
plays a crucial role in obtaining the required results. In the case of
supercritical growth ($r>3$), we obtain better results than that are available
in the literature for 2D Navier-Stokes equations.
