The position of a particle moving along x-axis depends on time according to the equation `x = at^2 +bt^3,` where x is in metre and t is in sec. What are the units and dimensions of a and b : what do they represent?

Answer

`ms^(-2), ms^(-2), LT^(-2) ; LT^(-3) ; acc.`
and rate of change of acc.

Explanation

`x = at^2 + bt^3`
Each term on RHS must have dimensions of x.
Therefore, `a = x//t^2 = m//s^2 =[LT^(-2)]`
'a' represents acceleration.
Also, `b =x//t^3 = m//s^3 = [LT^(-3)]`
`:. 'b'` represents rete of change of
acceleration with time.