Question

cheak the correctness of the equation v=u+at by dimensional analysis. where v.u.a& t represent final velocity.initial velocity .acceleration and time respectively.​

Answer 1

To Check:

Correctness of the equation : v = u + at , by dimensional analysis.

Verification:

For an equation to be dimensionally correct, the dimensions of the LHS should be equal to the dimensions of the RHS.

LHS :

$\therefore \: \{v \} = \{velocity \}$

$= > \: \{v \} = \{ {M}^{0} L{T}^{ - 1} \}$

RHS :

Only quantities of similar dimensions can be added.

$\therefore \: \{u \} = \{velocity \}$

$= > \: \{u\} = \{ {M}^{0} L{T}^{ - 1} \}$

Similarly :

$\therefore \: \{at \} = \{acc. \times time\}$

$= > \: \{at\} = \{ {M}^{0} L{T}^{ - 2} \times T\}$

$= > \: \{at\} = \{ {M}^{0} L{T}^{ - 1} \}$

So , both LHS and RHS is same , hence the equation is dimensionally correct.