1Which of these has the same dimensions as acceleration?
Acceleration and gravitational field intensity both have the dimensions [L T⁻²].
MechanicsClass 11, Motion in a Straight Line
Dimensional formula of Acceleration
[L T-2]
Change of velocity per unit time. The time is squared because velocity already has one time in it.
How to get the dimensional formula of acceleration
- Start from the definition: acceleration = velocity / time.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [L T-1] / [T].
- Add the powers of each base quantity: [L T-2].
Quantities with the dimensions [L T⁻²]
Equal dimensions do not make them the same quantity. Compare acceleration with the others in the full grid.
Three questions on acceleration
2What is the SI unit of acceleration?
The SI unit of acceleration is the metre per second squared (m/s²).
3Which one has different dimensions from the others?
Force is [M L T⁻²]. The other three are all [L T⁻²].
An equation that uses acceleration
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
s = u t + (1/2) a t2s[L]=ut[L]+1/2 at2[L]Dimensionally consistentEvery term is [L]
t = timea = acceleration
Acceleration: quick answers
What is the dimensional formula of acceleration?
The dimensional formula of acceleration is [L T⁻²]. It comes from acceleration = velocity / time.
What is the SI unit of acceleration?
The SI unit of acceleration is the metre per second squared (m/s²).
Which quantities have the same dimensions as acceleration?
Acceleration shares [L T⁻²] with acceleration due to gravity, gravitational field intensity. Equal dimensions do not make them the same quantity.