Using dimensional analysis, the expression v²/d has the same units as acceleration.
What is acceleration?
The time rate of change of the velocity is called the acceleration.
In dimensional analysis, any physical quantity is represented as [M^aL^bT^c]
For velocity, the dimensions can be written as [M⁰L¹T⁻¹]
For acceleration, the dimensions can be written as [M⁰L¹T⁻²]
If distance has the dimension [L], the dimension of v²/d will be [M⁰L¹T⁻¹]²/[L] = [M⁰L¹T⁻²]
This dimension is same as the dimension of acceleration.
Thus, the expression v²/d has the same units as acceleration.
Learn more about acceleration.
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