Question

check the correctness of equation S S=ut + 1a²t ​

Answer 1

Answer:

As per ques, for $S = ut + 1a^{2}t$

The dimensions of both LHS = RHS;

LHS;

     s = displacement = [$M^{0} L^{1} T^{0}$]

RHS;

 ut = velocity x time = $[M^{0} L^{1} T^{-1} ]$ x [$T^{1}$] = [$M^{0} L^{1} T^{0}$]

1$a^{2} t$ = $[M^{0} L^{2} T^{-4}]$

As LHS $\neq$ RHS

This formula is not correct, dimensionally.

Check for other one; s=ut+ $\frac{1}{2} at^{2}$

s = displacement = $[M^{0} L^{1} T^{0}]$

RHS;

 ut = velocity x time = $[M^{0} L^{1} T^{-1} ]$ x [$T^{1}$] = $[M^{0} L^{1} T^{0}]$

$\frac{1}{2} at^{2}$ = $[M^{0} L^{1} T^{-2}]$ x $[T^{2} ]$ = $[M^{0} L^{1} T^{0}]$

As LHS = RHS, formula correct dimensionally.

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