Understanding the SI Unit of Acceleration

The question asks about the power of the unit 'second' within the SI unit of acceleration. To answer this, we first need to know the standard SI unit for acceleration.

Acceleration is defined as the rate of change of velocity with respect to time. Velocity itself is the rate of change of displacement with respect to time.

Let's break down the units:

• Displacement is measured in meters (m), which is a fundamental SI unit.
• Time is measured in seconds (s), also a fundamental SI unit.
• Velocity is displacement divided by time, so its unit is meters per second (m/s or m s^-1).
• Acceleration is velocity divided by time, so its unit is (m/s) per second.

Mathematically, the unit of acceleration is:

\( \text{Unit of acceleration} = \frac{\text{Unit of velocity}}{\text{Unit of time}} = \frac{\text{m/s}}{\text{s}} \)

To simplify this expression, we can write it as:

\( \frac{\text{m}}{\text{s} \times \text{s}} = \frac{\text{m}}{\text{s}^2} \)

In SI base units, this is written as meters per second squared, or m/s².

When expressing units using negative exponents, we write m s^-2. This notation indicates that the unit 'second' is in the denominator and raised to the power of 2, which is equivalent to being in the numerator raised to the power of -2.

Comparing the standard SI unit notation m s^-2 with the general form of units expressed as powers of base units (e.g., m^a s^b), we can see the powers of each unit:

• The power of meter (m) is +1.
• The power of second (s) is -2.

The question specifically asks for the power of 'second' in the SI unit of acceleration. Based on our analysis, the power of second is -2.

Analyzing the Options

Let's look at the given options:

• Option 1: -2
• Option 2: 0
• Option 3: +1
• Option 4: -1

Our derivation shows that the power of 'second' in the SI unit of acceleration (m s^-2) is -2. This matches Option 1.

Conclusion

The SI unit of acceleration is meters per second squared (m/s²), which is written as m s^-2 in terms of negative exponents. In this notation, the unit 'second' has a power of -2.

Revision Table: Key Concepts for SI Units

Additional Information: Units and Dimensions in Physics

Understanding units and their powers is crucial in physics. The power of a unit tells us how that base quantity (like length or time) scales within the derived quantity. For instance, in acceleration (m/s²), the dependence on time is inverse squared (s^-2).

The powers of the base units in a derived unit are also related to the dimensions of the physical quantity. The dimension of acceleration is typically represented as [L T^-2], where [L] is the dimension of length (corresponding to meters) and [T] is the dimension of time (corresponding to seconds). The powers of L and T in the dimensional formula match the powers of the corresponding units (m and s) in the SI unit.

Being comfortable with unit analysis helps in checking the consistency of equations and understanding the physical meaning of quantities.