Let's restate the given problem carefully:
The velocity of a particle is given by
v=at+‌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+‌, 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−2]So,
[a]=[LT−2]Step 3. The second term
‌This term must also have the dimensions of velocity:
[‌]=[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]
