In the International System of Units, what is the SI unit of acceleration?

Introduction / Context:

This question is about the correct SI unit for acceleration, a fundamental quantity in mechanics. Acceleration describes how quickly velocity changes with time and appears in Newton second law, equations of motion, and many real world calculations such as vehicle performance or free fall problems. Using the correct unit is essential when applying these formulas.

Given Data / Assumptions:

• Acceleration is defined as rate of change of velocity with respect to time.
• Velocity itself has the SI unit metres per second.
• We work within the standard SI unit system.
• The options combine metres and seconds in different ways.

Concept / Approach:

Acceleration a is defined as change in velocity delta v divided by change in time delta t. If velocity is measured in metres per second (m/s) and time in seconds (s), then acceleration has units of (m/s) per second, which simplifies to m/s^2. This expresses how many metres per second the velocity changes in each second. Any unit that does not reflect this twofold division by time is incorrect for acceleration.

Step-by-Step Solution:

Verification / Alternative check:

In common problems, gravitational acceleration near the Earth surface is approximately 9.8 m/s^2. This value and unit combination appears in almost every physics textbook and example involving free fall, confirming that metres per second squared is the standard unit. In dimensional analysis, acceleration has dimensions of length divided by time squared, consistent with m/s^2. These checks reinforce that no other combination given in the options is correct for acceleration.

Why Other Options Are Wrong:

• Metres per second (m/s): This is the unit of velocity, not acceleration, as it involves only one division by time.
• Seconds per metre (s/m): This unit would correspond to the inverse of speed, sometimes used in wave contexts but not for acceleration.
• Seconds per metre squared (s/m^2): This has no standard interpretation as a basic kinematics unit.

Common Pitfalls:

Students may confuse velocity and acceleration because both involve metres and seconds. The key is to remember that acceleration is about how velocity changes, so it involves time twice. Writing acceleration as change in velocity over time and substituting units explicitly helps avoid mistakes. Keeping a small list of fundamental units in mind, such as m for distance, s for time, m/s for velocity and m/s^2 for acceleration, is a useful strategy.

Final Answer:

The SI unit of acceleration is metres per second squared, written as m/s^2.