Question

analyze why the si unit of acceleration is m/s²

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time.

Step2: Identify velocity unit

The SI - unit of velocity $v$ is meters per second ($m/s$) as velocity $v = \frac{\Delta x}{\Delta t}$ and SI - unit of displacement $\Delta x$ is meters ($m$) and of time $\Delta t$ is seconds ($s$).

Step3: Determine acceleration unit

Since $a=\frac{\Delta v}{\Delta t}$, substituting the unit of $\Delta v$ ($m/s$) and $\Delta t$ ($s$), we get $a=\frac{m/s}{s}=\frac{m}{s^{2}}$.

Answer:

The SI unit of acceleration is $\frac{m}{s^{2}}$ because acceleration is the rate of change of velocity with respect to time, and the unit of velocity is $m/s$ and time is $s$.