In mechanics, the physical quantity known as jerk is defined as the rate of change of acceleration with respect to time. What is the SI unit of jerk?

Introduction / Context:
In kinematics, we commonly study displacement, velocity, and acceleration. Jerk is a higher order quantity that describes how acceleration itself changes with time. It is particularly important in engineering applications where sudden changes in acceleration can cause discomfort or structural stress, such as in elevators, vehicles, and roller coasters. The question asks for the correct SI unit of jerk, which you can determine by analysing its definition in terms of more familiar quantities.

Given Data / Assumptions:

• Jerk is defined as the rate of change of acceleration with respect to time.
• Acceleration has SI unit metre per second square (m/s^2).
• Time has SI unit second (s).
• We apply basic dimensional analysis to find the unit of jerk.

Concept / Approach:
If a quantity is the rate of change of another quantity with respect to time, its unit is the unit of the original quantity divided by the unit of time. For example, velocity is the rate of change of displacement, so its unit is metres per second. Acceleration is the rate of change of velocity, so its unit is metres per second square. Jerk, being the rate of change of acceleration, has unit acceleration per unit time. Since acceleration has unit m/s^2, dividing by time (s) gives m/s^2 per s, which simplifies to m/s^3. Thus, the SI unit of jerk is metre per second cube (m/s^3).

Step-by-Step Solution:
Step 1: Write the definition of jerk: jerk = change in acceleration / change in time.Step 2: Note that the SI unit of acceleration is metre per second square, written as m/s^2.Step 3: Time has SI unit second, written as s.Step 4: The unit of jerk becomes (m/s^2) / s = m / (s^2 * s) = m/s^3.Step 5: Therefore, the SI unit of jerk is metre per second cube (m/s^3).

Verification / Alternative check:
Dimensional analysis provides a quick cross check. Displacement has dimension L. Velocity has dimension L T^-1. Acceleration has dimension L T^-2. Jerk, as the time derivative of acceleration, has dimension L T^-3. The SI combination that matches L T^-3 is metre per second cube, confirming that m/s^3 is the correct unit. No other combination among the options matches this dimension. This systematic approach avoids guessing based on appearance alone and ensures consistency with fundamental definitions.

Why Other Options Are Wrong:
Metre second, option A, would have dimension L T and is not associated with any standard kinematic quantity. Metre per second square, option C, is the unit of acceleration, not jerk. Metre per second, option D, is the unit of velocity. None of these represent the rate of change of acceleration. Only option B, metre per second cube (m/s^3), directly follows from the definition of jerk as acceleration per unit time.

Common Pitfalls:
Students often confuse jerk with acceleration and may mistakenly select metre per second square. Another common error is overlooking the extra division by time when moving from acceleration to jerk. To avoid such mistakes, remember the sequence: displacement (m), velocity (m/s), acceleration (m/s^2), jerk (m/s^3). Each step introduces an additional division by time. Writing out the units carefully during problem solving rather than relying on memory alone can greatly reduce errors in questions involving derived quantities like jerk.

Final Answer:
Metre per second cube (m/s^3)