Question #cb7bf

2 Answers

#a -> [L/(T*T)]#

#b -> [L/T]#

#c -> [T]#

Explanation:

I am considering the equation as :

#v = at + b * t/(t+c)#

Let me know if this is not what you meant.

In any equation, each term separated by #+# or #-# must have same dimension or else cannot be added.

So here #v# , #a*t# , and #b * t/(t+c)# must have same dimension. Since we know the dimension of velocity as #[L/T]#, the other 2 terms should also have the same dimension.

So #a*t# has dimension #[L/T]#

#[aT] = [L/T]#

#[a] = [L/(T*T)]#

Similarly, let us consider the denominator part of 2nd term. #(t + c)#. Here #t# and #c# must have the same dimensions since they are being added, so

#[c] = [T]#

The rest

#[b T/(c+T)] = [L/T]#

#[bT/T] = [L/T]#, since #c# and #T# are being added

#[b] = [L/T]#

Hope you have a good day.

Mar 30, 2017

The dimension of #a# and #b# is #=[L][T]^-1#
The dimension of #c# is #[T]#

Explanation:

The dimension of #c# is #[T]#

The dimension of #v# is #[L][T]^-1#

The dimension of #at# is #[L]#

The dimension of #a# is #[L][T]^-1#

The dimension of #b# is #[L][T]^-1#

I considered the equation as

#v=((at+bt))/((t+c))#

#LHS# is #=[L][T]^-1#

#RHS# is #=([L][T]^-1)/[T]*[T]#

Therefore,

#a# is #[L][T]^-1#