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.

The radiation of the fire causes the saucepan to heat up. the conduction of the saucepan then to distribute the heat over the saucepan and to give heat to the water. the convection of the water distributing the heat within the water, till all the water is boiling

I'm having some difficulty seeing the diagram clearly.but the question says there's a net inward force on the object.so we know right away,  from newton's 2nd law of motion, thatthat baby is accelerating.  it doesn't even matter which way thenet force is pointing.  if there's any net force, then either theobject's speed or else its direction must be changing.