Question

check dimensionally the correctness of following relation. V=u+at​

Answer 1

$\underline{\maltese \: {\sf AnsWer \: \maltese}}$

$:\implies\sf v = u + at$

• Dimensions of RHS = v
• Dimensions of LHS = u + at

$\dashrightarrow\:\:\sf [v] = \dfrac{[L]}{ [T]}$

$\dashrightarrow\:\:\sf [v] = [LT ^{ - 1} ]$

Now,

$\dashrightarrow\:\:\sf [u] = \dfrac{[L]}{ [T]}$

$\dashrightarrow\:\:\sf [u] = [LT ^{ - 1} ]$

Also,

$\dashrightarrow\:\:\sf [at] =\dfrac{[L]}{ [T^{2} ]} [T]$

$\dashrightarrow\:\:\sf [at] =[LT^{ - 2} ] [T]$

$\dashrightarrow\:\:\sf [at] =[LT^{ - 1} ]$

$\underline{\maltese \: {\textsf{\textbf{Dimensions of RHS = Dimensions of LHS}}}}.$