Position x vs Time t x_{o}(m) v_{o}
(m/s) a_{o}(m/s^{2})
da/dt(m/s^{3})

There is more information to gather from this type of curve. First, note
that the slope of the tangent starts up being positive, it becomes zero when the curve
reaches a maximum, then starts increasing in the negative direction. Before reaching the
maximum, the puck moves in the positive direction with a diminishing speed. It turns
around when the curve reaches maximum and starts moving with increasing speed in the
negative direction. Note that you can deduce from both parts that the acceleration is
negative. In the first portion (before reaching maximum,) since the velocity is
diminishing, we can deduce that the acceleration is in the opposite direction. We can then
deduce that it is negative since the velocity in that portion is positive.
In the second portion, after reaching maximum, since the velocity is increasing, we can
deduce that the acceleration is the same direction as the velocity.