This has puzzled me for a long time.
Consider an arbitrary object's motion in this graph. It has to accelerate each time its slope changes, but there is no curvature in the graph, which is a dead giveaway for acceleration in pos/time graphs. Its speed is constant here always, with the exception of at $t=0$, $t=2$, and $t=3.5$ (roughly). Its change in speed also seems nearly instant. I know this is an idealized object, and real motion would never be able to do this (no object can go from $5 \ m/s$ to $-15/3.5 \ m/s$ (roughly) instantaneously), but this kind of motion graph always puzzled me. It's taught pretty early on in kinematics yet it is glaringly unrealistic and unintuitive, I find, despite its simplicity.