  One-parameter solutions in supergravity carried by scalars and a metric trace
out curves on the scalar manifold. In ungauged supergravity these curves
describe a geodesic motion. It is known that a geodesic motion sometimes occurs
in the presence of a scalar potential and for time-dependent solutions this can
happen for scaling cosmologies. This note contains a further study of such
solutions in the context of pseudo-supersymmetry for multi-field systems whose
first-order equations we derive using a Bogomol'nyi-like method. In particular
we show that scaling solutions that are pseudo-BPS must describe geodesic
curves. Furthermore, we clarify how to solve the geodesic equations of motion
when the scalar manifold is a maximally non-compact coset such as occurs in
maximal supergravity. This relies upon a parametrization of the coset in the
Borel gauge. We then illustrate this with the cosmological solutions of
higher-dimensional gravity compactified on a $n$-torus.
