In the International System of Units (SI), the unit used to measure acceleration, that is the rate of change of velocity with time, is ______.

Introduction / Context:

Acceleration is a key concept in mechanics, describing how quickly velocity changes with time. It appears in Newton second law and in many kinematics problems. Knowing the correct SI unit for acceleration is essential for interpreting formulas and checking the dimensional consistency of physical equations. This question asks you to identify the correct SI unit from several similar looking options.

Given Data / Assumptions:

• Velocity in SI is measured in metres per second, written as m s^-1.
• Time is measured in seconds (s).
• Acceleration is defined as change in velocity per unit time.
• The SI system is being used throughout.

Concept / Approach:

Acceleration a is defined as Δv / Δt, where v is velocity and t is time. If velocity has units of m s^-1 and time has units of s, then acceleration has units (m s^-1) / s. This simplifies to m s^-2, that is, metre per second squared. In words, acceleration tells you how many metres per second the speed changes every second. The other options either represent velocity (m s^-1), are dimensionally incorrect, or refer to other physical quantities.

Step-by-Step Solution:

Verification / Alternative check:

Consider a car whose velocity increases from 0 to 10 m s^-1 in 2 seconds. The acceleration is a = (10 − 0) / 2 = 5 m s^-2. This means the speed increases by 5 metres per second every second. Writing it as m s^-2 matches our derived unit. Every standard physics text also lists m s^-2 as the SI unit of acceleration, confirming this result.

Why Other Options Are Wrong:

Option A (m s^-1): This is the SI unit of velocity, not acceleration.

Option C (m s^2): This would be metre times second squared, which does not correspond to any standard kinematic quantity.

Option D (m/s): This is another way of writing m s^-1, still velocity, not acceleration.

Option E (m^2/s): This unit is used in contexts like diffusion coefficient or kinematic viscosity, not for acceleration.

Common Pitfalls:

Students sometimes stop at m/s and forget that acceleration involves a second division by time, leading to m/s^2. It is helpful to say in words what the unit means: metres per second per second. The repetition of per second reminds you that the exponent on seconds must be squared in the denominator, giving s^-2. When in doubt, derive the units from the definition rather than trying to memorise them in isolation.

Final Answer:

The SI unit of acceleration is m s^-2 (metre per second squared).