Question

find the dimensions of unknown physical quantity a, b, c, d? v=a+ct2+dt3

Answer 1

I hope it helps u out but I couldn't find b in the question itself

Answer 2

Since we have known velocity is displacement upon time; given equation is

$v=a+c{ t }^{ 2 }+d{ t }^{ 3 }$

If we assume all the vectors have same direction, we get v=a; $v= c{ t }^{ 2 }; v=d{ t }^{ 3 }$

For v=a;

$\frac { D }{ t } =a\quad \Rightarrow a=D{ t }^{ -1 }$

For $v= c{ t }^{ 2 };$

$\frac { D }{ t } = c{ t }^{ 2 }\quad \Rightarrow c=\frac { D }{ { t }^{ 3 } }\quad or\quad D{ t }^{ -3 }$

For $v=d{ t }^{ 3 };$

$\frac { D }{ t } = d{ t }^{ 3 }\quad \Rightarrow d=\frac { D }{ { t }^{ 4 } }\quad or\quad D{ t }^{ -4 }$

Hence the dimensions of a, c and d are achieved as $D{ t }^{ -1 }, D{ t }^{ -3 }, D{ t }^{ -4 }$.