Question

v=at+b/t+c+v is a dimensionally valid equation. Obtain the dimensional formula for a, b and c where v is velocity, t is time.

Answer 1

v = at + b/t + c + v' is dimensionally valid equation. here v is velocity and t is time.

from dimensional analysis

dimension of v = dimension of (at) = dimension of (b/t) = dimension of c

case 1 : dimension of v = dimension of (at)

or, [LT-¹] = dimension of a × dimension of t

or, [LT-¹] = dimension of a × [T]

or, dimension of a = [LT-¹]/[T] =[LT-²]

case 2 : dimension of v = dimension of (b/t)

or, [LT-¹] = dimension of b/dimension of t

or, [LT-¹] = dimension of b/[T]

or, dimension of b = [LT-¹][T] = [L].

case 3 : dimension of v = dimension of c

or, [LT-¹] = dimension of c

or, dimension of c = [LT-¹]

Answer 2

v = at + b/t + c + v' is dimensionally valid equation. here v is velocity and t is time.

from dimensional analysis

dimension of v = dimension of (at) = dimension of (b/t) = dimension of c

case 1 : dimension of v = dimension of (at)

or, [LT-¹] = dimension of a × dimension of t

or, [LT-¹] = dimension of a × [T]

or, dimension of a = [LT-¹]/[T] =[LT-²]

case 2 : dimension of v = dimension of (b/t)

or, [LT-¹] = dimension of b/dimension of t

or, [LT-¹] = dimension of b/[T]

or, dimension of b = [LT-¹][T] = [L].

case 3 : dimension of v = dimension of c

or, [LT-¹] = dimension of c

or, dimension of c = [LT-¹]

so this is the answer of your asked question

hope it helps you :)