One student doubts the expression for kinetic energy as MV3 or Kinetic

Energy = ½ MV2. How can you help him with the help of dimensional

According to question kinetic energy(K) depends on mass(m) and speed(v).

So, K α ma

and K α vb

Where a and b are costants.

After combining

K α ma vb.

K = k ma vb.  ......................(1)

Where k = constant.

Dimensions for K, m and v

[K] = [MLT-2]

[m] = [M]

[v] = [LT-1]

k is dimensionless.

Eqn (1) becomes after taking dimension

[MLT-2] =  [M]a [LT-1]b

=> [MLT-2] = [MaLT-b

After comparing the power of M, L and T.

a = 1

b = 2

So, KE = k MV2

Hence, according to your question 

KE = (1/2)MV2

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