Short Answer 
The relationship between distance and time for a car’s movement is represented by the formula D = kT, where k is a constant reflecting speed. By analyzing the time taken to cover two kilometers, we determined that k equals 4/3, leading to the speed equation D = (4/3)T.
Step 1: Understanding Distance and Time Relationship
The distance D that a car travels is directly proportional to the time T it moves. This relationship can be expressed with the formula D = kT, where k represents the constant of proportionality. Thus, the longer the car moves, the greater the distance it covers, and the value of k will determine the speed.
Step 2: Determine the Coefficient of Variation (k)
To find the value of k, we can utilize the time taken to cover certain distances. We have two key pieces of information: the car travels the first kilometer in 20 seconds and the second kilometer in 30 seconds. By substituting these values into the formula:
- For the first kilometer: 1 = k * 20
- For the second kilometer: 2 = k * 30
Step 3: Solve for k and Calculate Speed
Now, we can solve for k by dividing the equations derived from the two distance-time relationships. This simplifies our calculations:
- By dividing: (2/1) = (k * 30)/(k * 20)
- Simplifying gives: 2 = (3/2)*k
- Finally, solving for k results in k = 4/3.
Thus, the speed of the car can be expressed using the formula D = (4/3)T.