13. The distance, D, travelled by a particle is directly proportional to the square of the time, t, taken.
When t = 40, D = 30
(a) Find a formula for D in terms of t.
(b) Calculate the value of D when t = 64
(c) Calculate the value of t when D = 12
Give your answer correct to 3 sig fig.
By definition, two quantities are directly proportional if one is a constant times the other. so saying that D is proportional to t^2 is saying that
That is the general formula for proportional quantities. Now to answer specific questions, we need to know exactly what the constant is. Dan used the two given values of D and t to find k, so now we just replace that k in the general formula.
Since we found that , we can plug it in to the formula, so:
Now we can use this to answer all the questions. Since now we have only two unknowns, it means that if we are given one of the unknowns, we can easily solve for the other