Question

Question #cb7bf

Answer 1

`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.

Answer 2

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`