What is the dimension of (½)at2?

Answer:

½ a t2 has the dimension of length since the dimension of acceleration is L/T2 and multiplying it by T2 leaves us with the dimension of length.

Dimensions of Acceleration

The dimensional formula of acceleration is given by MLT-2

Where,

  • M = Mass
  • L = Length
  • T = Time

Dimensions of Time Period

The dimensional formula of Time Period is given by [M0 L0 T1]

Where,

  • M = Mass
  • L = Length
  • T = Time

½ a t

⇒ 1/2 [MLT-2] [M0 L0 T1] [M0 L0 T1]

⇒ 

\(\begin{array}{l}\frac{1}{2}\times \frac{L^{1}}{T^{2}}\times ^{T^{2}}\end{array} \)

⇒ 1/2 [L]

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