Question

What is the 'SI' unit of acceleration ?

• A. KMSec$^{-1}$
• B. KM/Sec$^{-1}$
• C. MS$^{-1}$
• D. MS$^{-2}$

Hint:

Remember the definitions: Speed is distance/time, velocity is displacement/time, and acceleration is change in velocity/time. This helps in deriving their respective units.

Answer 1

The Correct Option is D

Step 1: Define acceleration.
Acceleration is the rate of change of velocity with respect to time. Velocity is a vector quantity representing the rate of change of position, and it has units of length per unit time. Step 2: Determine the SI units of length and time.
In the International System of Units (SI), the base unit for length is the meter (m), and the base unit for time is the second (s). Step 3: Determine the SI unit of velocity.
Velocity is displacement divided by time. So, the SI unit of velocity is meters per second (m/s), or MS$^{-1}$. Step 4: Determine the SI unit of acceleration.
Acceleration is change in velocity divided by time. Therefore, the SI unit of acceleration is the unit of velocity divided by the unit of time:
$\frac{\text{m/s}}{\text{s}} = \frac{\text{m}}{\text{s}^2}$
This can also be written as MS$^{-2}$.
Step 5: Compare with the given options.
(1) KMSec$^{-1}$: Kilometers per second, which is a unit of speed or velocity, not acceleration.
(2) KM/Sec$^{-1}$: Kilometers per second, same as (1).
(3) MS$^{-1}$: Meters per second, which is the unit of speed or velocity.
(4) MS$^{-2}$: Meters per second squared, which is the correct SI unit for acceleration. (4) MS$^{-2$}