Question

Check the dimentional consistency of the equation v+u+at and hence show that equation is dimentionslly correct.Here v is final velocity,u is initial velocity,a is acceleration and t is time interval.​

Answer 1

Answer :-

Equation :-

v = u + at

where

• v is final velocity.
• u is initial velocity.
• a is acceleration.
• t is time.

For this equation to be dimensionally correct, the dimension of v should be equal to dimension of u and dimension of at.

Dimension of v ( final velocity ) = LT⁻¹

Dimension of u ( initial velocity ) = LT⁻¹

Dimension of at ( acceleration × time ) =

LT⁻² × T¹ = LT⁻¹

Dimension of velocity = Dimension of initial velocity = Dimension of acceleration × time

LT⁻¹ = LT⁻¹ + LT⁻¹

Hence, the equation is dimensionally correct.

Answer 2

✴ Answer ✴

✮ meaning of symbol

• Here you represent the velocity, V the final velocity, a the uniform acceleration, and t is the time.

✯ Formulae

• The Dimensional formula of u is [M°LT-¹]
• The Dimensional formula of v is [M°LT-¹]
• The Dimensional formula of at is [M°LT-²][T] = [M°LT-¹]

Required answer

Here the dimensions of every term in the given physical relation are the same, hence the given physical relation is dimensionally correct.

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