Final answer:
To express d in terms of t given that D is directly proportional to the square of t and d = 80 when t = 4, we use the formula D = k * t^2. By finding the value of k, we can substitute it into the equation to express d in terms of t.
Step-by-step explanation:
To express d in terms of t given that D is directly proportional to the square of t and d = 80 when t = 4, we can use the formula for direct proportionality: D = k * t^2. We need to find the value of k to substitute it in the equation.
Substituting d = 80 and t = 4 into the equation, we can find k. 80 = k * 4^2. Solving for k, we get k = 5.
Finally, we can express d in terms of t by substituting k = 5 into the equation: d = 5 * t^2.