Question

the velocity v of a particle is given in the term of time is v =at +b/t+c the dimensions of a, b, c are:​

Answer 1

Given equation is,

$\displaystyle\longrightarrow\sf {v=at+\dfrac {b}{t+c}}$

According to the Principle of Homogeneity,

$\displaystyle\longrightarrow\sf {[v]=[a][t]\implies\underline {\underline {[a]=\dfrac {[v]}{[t]}=LT^{-2}}}}$

And,

$\displaystyle\longrightarrow\sf {\underline {\underline {[c]=[t]=T^{-1}}}}$

And,

$\displaystyle\longrightarrow\sf {[v]=\dfrac {[b]}{[t]}\implies\underline {\underline {[b]=[v][t]=L}}}$