In kinematics, acceleration is defined as the rate of change of which physical quantity with respect to time?

Introduction / Context:
Kinematics deals with the description of motion without considering its causes. Acceleration is one of the key concepts, and students must clearly understand what quantity it describes the rate of change of. This question checks if you can correctly link acceleration to the time rate of change of velocity, not just speed or other higher-order derivatives such as jerk or jounce.

Given Data / Assumptions:
- The options include speed, velocity, jerk and jounce.
- Standard definitions from one-dimensional and three-dimensional motion are assumed.
- Time is the independent variable in these rate-of-change definitions.

Concept / Approach:
Velocity is a vector quantity that has both magnitude and direction. Acceleration is defined as the rate of change of velocity with respect to time, which can involve change in speed, change in direction, or both. Speed alone is a scalar; its time rate of change is not the full acceleration unless direction is constant. Jerk is the rate of change of acceleration with time, and jounce is the rate of change of jerk. Therefore, the basic definition of acceleration must be tied to velocity, not to speed, jerk or jounce.

Step-by-Step Solution:
Step 1: Recall the definition: acceleration a = change in velocity / change in time. Step 2: Recognise that velocity includes both speed and direction; so acceleration describes how this vector quantity changes. Step 3: Speed alone is only the magnitude of velocity; change in speed is not the complete description of acceleration if direction changes. Step 4: Jerk is the time derivative of acceleration, and jounce is the time derivative of jerk, so they are higher-order derivatives. Step 5: Therefore, acceleration is the rate of change of velocity with respect to time.

Verification / Alternative check:
In calculus notation, velocity v is the first derivative of displacement with respect to time, and acceleration a is the first derivative of velocity with respect to time (or the second derivative of displacement). This is written as a = dv/dt. This mathematical relationship confirms that acceleration is directly related to how velocity changes over time, not how jerk or jounce change.

Why Other Options Are Wrong:
Speed: While a change in speed may contribute to acceleration, acceleration is defined in terms of velocity, which includes direction. Constant speed in a circular path still produces acceleration due to change in direction, illustrating why speed alone is insufficient.
Jerk: Jerk is defined as the rate of change of acceleration with respect to time, not the rate of change of velocity.
Jounce: Jounce is the rate of change of jerk with time, an even higher-order derivative, and not the definition of acceleration.

Common Pitfalls:
Students sometimes think acceleration only occurs when speed changes, ignoring change in direction. This leads them to confuse speed and velocity in definitions. It is vital to remember that velocity is a vector and that acceleration measures how this vector changes. Another trap is to memorise terms like jerk or jounce without understanding the hierarchy: velocity, acceleration, jerk and then jounce as successive time derivatives of position.

Final Answer:
Acceleration is defined as the rate of change of velocity with respect to time.