Answer :
In AP Physics 1 principles, acceleration and velocity vectors in simple harmonic motion are related such that acceleration is proportional to displacement and acts in the opposite direction, with acceleration maximum at maximal displacement and zero at equilibrium. Velocity is maximum at equilibrium and zero at maximal displacement.
In AP Physics 1, the relationship between acceleration and velocity vectors in simple harmonic motion is defined by oscillating motion where acceleration is proportional and opposite to displacement. This stems from the classic example where an object in uniform circular motion has its motion projected onto an axis, thereby undergoing simple harmonic motion (SHM). According to this model, the velocity of the object is maximal at the equilibrium position and zero at maximal displacement, while the acceleration is zero at the equilibrium position and maximal at maximal displacement, acting always in the opposite direction to the displacement.
Acceleration in SHM always points towards the center of the circular path in the uniform circular motion analogy, which also corresponds to the equilibrium position in SHM. As per Hooke's Law, which governs the restoring force in systems like springs, acceleration increases as the object moves away from the equilibrium position. The graphs of position (x(t)), velocity (v(t)), and acceleration (a(t)) as a function of time (t) for an object on a spring can help visualize these relationships.
For an object experiencing simple harmonic motion, the acceleration and velocity vectors are therefore always perpendicular at the equilibrium position where velocity is maximum and acceleration is zero. As the object moves toward maximum displacement, the acceleration vector grows and points opposite to the direction of velocity, reflecting the restoring force.
