# What do you mean by $5 \mathrm{~m} \mathrm{~s}^{-2}$ ?

$5m{s}^{-2}$ represents the acceleration $(a)$.

$\because\ Acceleration (a)=\frac{Change in velocity (m/s)}{Time(measured\ in\ s)}$

Therefore, the unit of acceleration will be given as-

$Acceleration (a)=\frac{m/s}{s}$

$Acceleration (a)=\frac{m}{s\times s}$

$Acceleration (a)=\frac{m}{s^2}$

$Acceleration (a)=m/s^2$                      [slash (/) represent division]

$Acceleration (a)=m{s}^{-2}$          [as we put the denominator with numerator the power will be written with the negative sign $m{s}^{-2}$ ]

Explanation

We know that,

Acceleration is the change in velocity divided by time. Velocity consists of the unit m/s (means m is divided by s) because velocity is equal to displacement divided by time. And, displacement keeps the unit meter (m) or kilometer (km), while time keeps the unit second (s) or hour (h).

$Velocity=\frac{Displacement(measured\ in\ m\ or\ km)}{Time(measured\ in\ s\ or\ h)}$

So, the unit of velocity is given as-

$Velocity=\frac{m}{s}\ or\frac{km}{h}$

$Velocity=m/s\ or\ km/h$

$Velocity=m{s}^{-1}\ or\ km{h}^{-1}$   [as we put the denominator with numerator the power will be written with the negative sign $m{s}^{-2}$ ]

Now, we know that-

$Acceleration (a)=\frac{Change in velocity (m/s)}{Time(measured\ in\ s)}$

Here,

As the velocity is measured in $m/s$ or $m{s}^{-2}$, the change in velocity also keeps the same unit.

$[\because\ Change in velocity=\ final velocity(m/s) - initial velocity(m/s)]$.

Therefore,

$Acceleration (a)=\frac{Change in velocity (m/s)}{Time(measured\ in\ s)}$

Therefore, the unit of acceleration will be given as-

$Acceleration (a)=\frac{m/s}{s}$

$Acceleration (a)=\frac{m}{s\times s}$

$Acceleration (a)=\frac{m}{s^2}$

$Acceleration (a)=m/s^2$                      [slash (/) represent division]

$Acceleration (a)=m{s}^{-2}$         [as we put the denominator with numerator the power will be written with the negative sign $m{s}^{-2}$ ]

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Updated on: 10-Oct-2022

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