Dimension of acceleration

May 21, 2026Physics

ScanSolve AI Answer

Answer

[L][T^{-2}]

5 steps

Define acceleration.
Acceleration is the rate of change of velocity.
$a = \frac{\Delta v}{\Delta t}$
Define velocity.
Velocity is the rate of change of displacement (or distance).
$v = \frac{\Delta d}{\Delta t}$
Substitute the definition of velocity into the acceleration formula.
$a = \frac{\left(\frac{\Delta d}{\Delta t}\right)}{\Delta t} = \frac{\Delta d}{(\Delta t)^2}$
Determine the fundamental dimensions for displacement and time.
The dimension of displacement ( $\Delta d$ ) is length, denoted by $[L]$ .
The dimension of time ( $\Delta t$ ) is time, denoted by $[T]$ .
Substitute the fundamental dimensions into the acceleration formula.
Dimension of acceleration = $\frac{[L]}{[T]^2} = [L][T^{-2}]$

Thus, the dimension of acceleration is $[L][T^{-2}]$ .