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

analysis

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

So, K α m^a

and K α v^b

Where a and b are costants.

After combining

K α m^a v^b.

K = k m^a v^b.  ......................(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] = [M^aLT^-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