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Direct proportion to the square root

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Scaffolded worksheet on direct proportion
Scaffolded worksheet on direct proportion

Direct proportion to the square root occurs when one quantity changes in proportion to the square root of another. This concept is useful in physics and engineering, such as understanding the relationship between speed and stopping distance, or pressure and volume in gases. It helps in solving problems where changes happen more gradually as one value grows. Jump to the questions

Practise now

Question

y is directly proportional to √p

y = when p =

Find the equation for y and p

Step 1 - describe the relationship using the correct symbol

y ∝ √p

Step 2 - replace the symbol with the constant of proportionality, k

y = √p

Step 3 - substitute the values from the question into the equation

= k

Step 4 - rearrange the equation to isolate k

/ = k

Step 5 - determine the value of k

k =

Step 6 - write the final equation linking y and √p

y = √p

Find y when p =

Step 1 - restate the equation

y = √p

Step 2 - substitute the value you know

y = ×

Step 3 - determine the final value of y

y =

Find p when y =

Step 1 - restate the equation

y = √p

Step 2 - substitute the value you know

= × √p

Step 3 - rearrange the equation to isolate √p

/ = √p

Step 4 - calculate the value of √p

√p =

Step 5 - calculate the value of p

p =