Question

What is the dimensional formula of acceleration?

Answer 1

Solution:

1. Acceleration is the change in velocity with respect to time and its formula is as follows: $a=\frac{dv}{dt}$, where v is the velocity of the body and t is the time taken.
2. Moreover, velocity can be defined as the rate of change in displacement with respect to time and its formula is as follows: $v=\frac{dS}{dt}$, where S is the displacement of the body.
3. Thus, the dimensional formula of velocity will be: $velocity=\frac{\left[Length\right]}{\left[Time\right]}=\frac{\left[L\right]}{\left[T\right]}=\left[L{T}^{-1}\right]$
4. Now, let us calculate the dimensional formula of acceleration: $acceleration=\frac{\left[velocity\right]}{\left[time\right]}=\frac{\left[L{T}^{-1}\right]}{\left[T\right]}=\left[L{T}^{-2}\right]$

Thus, the dimensional formula of acceleration will be $\left[L{T}^{-2}\right]$.