Which of the following is the unit of acceleration?

Question

Examoogle · Accepted Answer

The correct answer is Option C: $m/s^2$. Acceleration is defined as the rate of change of velocity with respect to time. The SI unit of velocity is metre per second ($m/s$) and time is second ($s$), so the SI unit of acceleration is metre per second squared ($m/s^2$).

Step-by-Step Solution & Concepts:
Acceleration is defined as the rate of change of velocity with respect to time. The SI unit of velocity is metre per second ($m/s$) and time is second ($s$), so the SI unit of acceleration is metre per second squared ($m/s^2$).

Working Principle: Acceleration ($a$) is mathematically expressed as the derivative of velocity ($v$) with respect to time ($t$), or the change in velocity divided by the time interval. Thus, its dimensional formula is $[L T^{-2}]$ and its standard SI unit is $m/s^2$ or $m \cdot s^{-2}$.

Key Formulas: $a = \frac{v - u}{t}$ — Acceleration formula in terms of initial velocity $u$, final velocity $v$, and time $t$; $[a] = [L T^{-2}]$ — Dimensional formula of acceleration

Key Points: Acceleration is a vector quantity having both magnitude and direction.; The SI unit is metre per second squared ($	ext{m/s}^2$).; Negative acceleration is often called retardation or deceleration.

Applications: Calculating motion of falling bodies under gravity ($g \approx 9.8 	ext{ m/s}^2$); Designing high-speed transit systems and bullet trains

Additional Info: Speed/Velocity has the unit $	ext{m/s}$.. Force has the unit $	ext{kg} \cdot 	ext{m/s}^2$ or Newton (N).

Answer: C is correct — metre per second squared ($m/s^2$) is the standard SI unit of acceleration.

Exam Tip: Always verify dimensional formulas: acceleration is distance divided by time squared ($L/T^2$), which directly yields $	ext{m/s}^2$.

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