If variation of position with time t is given by x = a + bt + ct2 . Write the dimensions of a, b & c.

The given equation is x = a + bt + ct^2, which is a position-time relation.

1. The dimension of 'x' (position) is [M^0 L^1 T^0] because position is measured in length.

2. 'a' is the initial position, so it has the same dimension as 'x', which is [M^0 L^1 T^0].

3. 'b' is multiplied by 't' (time) in the equation. So, to make the dimensions on both sides of the equation equal, 'b' must have the dimensions of position divided by time, which is [M^0 L^1 T^-1].

4. 'c' is multiplied by 't^2' (time squared) in the equation. So, to make the dimensions on both sides of the equation equal, 'c' must have the dimensions of position divided by time squared, which is [M^0 L^1 T^-2].