Question

if x=at 2 +bt+c where x is displacement as function of time, then give the dimension of a and c

Answer 1

dimension of a=LT-2
dimension of b= LT-1
dimension of c =L

Answer 2

Answer:

a = $[L][T^{-2}]$ ; b = $[L][T^{-1}]$ and c = $[L]$

Explanation:

For any equation to be Dimensionally accurate, all terms on both sides should have the same dimensions even if they are spread across addition or subtraction.

This means dimensions for:-

$x = at^{2} = bt = c \\ \\ [L] = [a][T^{2}] = [b][T]=[c]$

This implies that:-

a has to have dimensions as $[L][T^{-2}]$
b has to have dimensions as $[L][T^{-1}]$
c has to have dimensions as $[L]$

If we use these dimensions for a,b and c. All terms on both the sides have the same dimensions as 'x' i.e. displacement.