Question

the instantaneous acceleration of an object is
the rate of change of speed at an instant of time.
the rate of change in velocity at an instant of time.
the rate of change of position at an instant of time
the rate of change of time at an instantaneous position.

Explanation:

To determine the correct definition of instantaneous acceleration, we recall the physics concept: acceleration is the rate of change of velocity. Instantaneous acceleration is this rate at a specific instant in time.

• The green option refers to rate of change of speed (speed is scalar, acceleration involves velocity which is vector, so incorrect).
• The orange option describes velocity (rate of change of position), not acceleration.
• The cyan option is incorrect as it misrepresents the concept.
• The blue option correctly states that instantaneous acceleration is the rate of change of velocity at an instant of time.

Answer:

the rate of change in velocity at an instant of time. (the blue - colored option)