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If v = u + at , where v is final velocity and u is initial velocity and t is time in seconds, a is acceleration, then the dimensions of a is

If v = u + at , where v is final velocity and u is initial velocity and t is time in seconds, a is acceleration, then the dimensions of a is Correct Answer LT<sup>-2</sup>

CONCEPT:

Principle of homogeneity of dimensions:

  • According to this principle, a physical equation will be dimensionally correct if the dimensions of all

          the terms occurring on both sides of the equation are the same.

  • This principle is based on the fact that only the physical quantities of the same kind can be

           added, subtracted, or compared.

  • Thus, velocity can be added to velocity but not to force.

EXPLANATION:

Given that, v = u + at

  • From the principle of dimensional homogeneity, the left-hand side of the equation dimensionally

          equal to the right-hand side of the equation.

  • The dimension formula of velocity (v) =  

Hence, = u

  • Therefore dimension of  'u' is .

For the second term

= aT

=> a = / T =

Therefore the dimension of a is

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