Harder Proportion – Direct and Inverse Relationships | Pearson Edexcel International GCSE Maths
These two examples use proportional relationships involving square roots. In each case, the proportional statement is first converted into an equation containing a constant of proportionality, k . The given values are then used to find k before the required value is calculated. Question 1 – Direct Proportion and Square Roots The time t seconds taken for a stone to fall is directly proportional to the square root of the distance d metres. When t = 4.6 , d = 25 . (a) Express t in terms of d . (b) Find the time taken when d = 42.25 . (a) Express t in terms of d t ∝ √d ⇒ t = k√d when t = 4.6, d = 25 ⇒ 4.6 = k√25 ⇒ 4.6 = 5k ⇒ k = 4.6 / 5 ∴ k = 0.92 t = 0.92√d ...