Question

The distance covered by a particle in time t while starting with the initial velocity u and moving with a uniform acceleration a is given by s= ut+(1/2)at^2. Check the correctness of the expression using dimensional analysis.

Answer 1

HEYA!!
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⏪DIMENSIONAL ANALYSIS ⏪
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↪To Check the Correctness of the Given Equation , we use the Principle of Homogenity that states that dimensions of two sides of a given physical relation must be same .

Now, Given Equation is

$s = ut + \frac{1}{2} at {}^{2}$
Now, For LHS.

We have Distance S . so dimensions of Distance are [ L ] ---------------(1)


Also, For RHS we have ,

By applying the Dimensions of Velocity , Acceleration and Time;


[ LT^-1 ] [ T ] + 1/2 [ LT^-2] [ T^2 ]

[ L ]. + 1/2 [ L ]

Now , Length added to length gives Length only . So we have RHS= [ L ]--------(2)



From (1) and (2)

LHS=RHS.

Hence the relation is dimensionally correct .


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