Zero velocity is not zero acceleration

01
The tempting model
Concluding a = 0 at the instant an object is momentarily at rest.
02
Why it feels right
If it's not moving, it seems like nothing is changing.
03
Where it breaks · how to catch it
You set acceleration to zero at a turning point (top of a toss, ends of an oscillation).
04
The correct model
Acceleration is set by the net force, not the current speed. At the top of a toss v = 0 but a = −g; at the extremes of SHM speed is zero yet acceleration is maximal.
05
Repair · see it, then test it
worked example At the peak of its flight, what is a thrown ball's acceleration?
Tempting move
Zero — it's momentarily stopped.
Correct move
−g downward; gravity never switches off.
Test the repair NL-03 · transfer

At the leftmost turning point of a horizontal spring oscillator, the cart is instantaneously at rest. Its acceleration points:
Nowhere; it is zero Toward equilibrium Away from equilibrium Along its previous velocity

Make a fresh prediction before referring to the worked example.