Let's restate the given problem carefully: The velocity of a particle is given by v=at+‌
b
t+c
We need to find the dimensions of a,b, and c. Step 1. Dimensional formula of velocity [v]=[LT−1] Step 2. Dimensional analysis of first term at In the expression v=at+‌
b
t+c
, both terms on the right-hand side must have the same dimensions as velocity. The first term: at ‌[a][t]=[v]=[LT−1] ‌[a]=‌
[LT−1]
[T]
=[LT−2] So, [a]=[LT−2] Step 3. The second term ‌
b
t+c
This term must also have the dimensions of velocity: [‌
b
t+c
]=[LT−1] Now, t+c is a sum - you can only add quantities with the same dimensions, so: [c]=[t]=[T] Then, [b]=[LT−1]⋅[t+c]=[LT−1]⋅[T]=[L] So, [b]=[L] Final Dimensions: [a]=[LT−2],‌‌[b]=[L],‌‌[c]=[T]