Question

the velocity v of a particle depends on time t as V=At^2 +Bt.Find dimensions and units of A and B?​

Answer 1

Answer:

[A] = [L T^-3] and [B] = [L T^-2]

Solution:

The velocity V of a particle depends on time 't' as V = At² + Bt  

Note:  

Vectors of only same dimensions can be added or subtracted.

Since, L.H.S. = R.H.S.

We can get, [A] = [L T^-1]/[T²]

Also [B] = [L T^-1]/[T]

Therefore, [A] = [L T^-3] and [B] = [L T^-2]

The dimensions of A are [L T^-3] and the dimensions of B are [L T^-2].