Question

the velocity (v) of a particle varies with time (t) as v=at^{2} +b/t+c find the dimension of a,b,c

Answer 1

As velocity must be in m/s and all the terms are being added, all the term's units must be m/s.
$a {t}^{2} =m{s}^{ - 1}$
So,
$a {s}^{2} = m {s}^{ - 1}$
$a = m {s}^{ - 3}$
or
$a = ( {m}^{0} {l}^{1} {t}^{ - 3})$
similarly you'll get,
$b = ( {m}^{0} {l}^{1} {t}^{0} )$
and
$c = ({m}^{0} {l}^{1} {t}^{ - 1} )$
Where, m=mass, l=length, t=time.