Ineed setting this problem up. ! a mother pushes a stroller up a hill, with the center of the stroller 1 meter ahead of her body. she maintains contact with the stroller at all times. her position is x(t), speed is v(t) and her acceleration is a(t). what are the position, velocity, and acceleration of the stroller at any time t?

The only thing you can derive ...maybe ... from the given information is that
the stroller's x(t) is 1 + the mother's x(t).  And if her progress is not strictly
along the x-axis, then even that statement isn't true.

If the stroller's v(t) and a(t) were not identical to the mother's v(t)and a(t), then
mother and stroller would "come apart".  But you've told us that they're always
in contact, so their v(t) and a(t) must be identical.

A slightly more rigorous (and mathematical) argument is that since the mother's
and the stroller's x(t) differ (at most) only by a constant, then their derivatives
x'(t) (which is v(t)) and x''(t) (which is a(t)) are equal.