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Check the correctness of S=ut + 1/2 at2

Using dimensional anaylaysis you can check the correctness of the equation , but the drawback is you wont be able to check the dimensionless constant (here 2).

the dimension of each term in the equation on RHS and also the term on LHS should be same.

Dimension on LHS [ M0L1To]

Dimension on RHS

[ut] = [M0L1T-1][M0L0T1] = [M0L1T0]

[at2] = [M0L1T-2][M0L0T2] = [M0L1T0]

Since dimensions on LHS = dimension onRHS ; equation is correct

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To Prove - s = ut + 1/2 at2

We know that , Average Velocity = Initial Velocity + Final Velocity / 2

 Average Velocity = u + v / 2

We know that, Distance travelled = Average Velocity * time

s = { u + v } /2 * t

From first equation of motion we know that v = u + at. So writing u + at in place of v we get

s = { u + u + at } / 2 * t

s = { 2u + at } / 2 * t

s = 2ut + at2 / 2

s = ut + 1/2 at 2

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