1Which of these has the same dimensions as velocity?
Velocity and escape velocity both have the dimensions [L T⁻¹].
MechanicsClass 11, Motion in a Straight Line
Dimensional formula of Velocity
[L T-1]
Distance covered per unit time. Speed has the same dimension, velocity adds a direction.
How to get the dimensional formula of velocity
- Start from the definition: velocity = length / time.
- Put in the dimension of each part: [L] / [T].
- Add the powers of each base quantity: [L T-1].
Quantities with the dimensions [L T⁻¹]
Equal dimensions do not make them the same quantity. Compare velocity with the others in the full grid.
Three questions on velocity
2What is the SI unit of velocity?
The SI unit of velocity is the metre per second (m/s).
3Which one has different dimensions from the others?
Density is [M L⁻³]. The other three are all [L T⁻¹].
An equation that uses velocity
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
Velocity: quick answers
What is the dimensional formula of velocity?
The dimensional formula of velocity is [L T⁻¹]. It comes from velocity = length / time.
What is the SI unit of velocity?
The SI unit of velocity is the metre per second (m/s).
Which quantities have the same dimensions as velocity?
Velocity shares [L T⁻¹] with escape velocity, root mean square velocity, speed of light. Equal dimensions do not make them the same quantity.