The following graph shows the position of a car versus time. When is the car traveling the fastest?

Question

A graph of the journey of a car with time (hours) on the horizontal axis and distance (km) on the vertical axis. A line slanting to the right connects the points (0, 0) and (1, 20). Another line with a steeper slope. Connects (1, 20) and (3, 80). A steeper slanted line connects (3, 80) and (4, 0).

Source: PDQ Digital Media Solutions Ltd. Pearson Education Ltd

(1 point)
Responses

Between hours 1 and 2
Between hours 1 and 2

Between hours 2 and 3
Between hours 2 and 3

Between hours 0 and 1
Between hours 0 and 1

Between hours 3 and 4
Between hours 3 and 4
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Answer 1

To determine when the car is traveling the fastest, we need to analyze the slopes of the lines in the graph, as the slope represents the car's speed (distance covered over time).

1. Between hours 0 and 1: The line rises from (0, 0) to (1, 20), which gives a slope of (20-0)/(1-0) = 20 km/hour.

2. Between hours 1 and 3: The line rises from (1, 20) to (3, 80), which gives a slope of (80-20)/(3-1) = 30 km/hour.

3. Between hours 3 and 4: The line goes down from (3, 80) to (4, 0), which gives a slope of (0-80)/(4-3) = -80 km/hour (the car is moving backward, indicating a stop or a return).

From the slopes calculated, the fastest speed occurs between hours 1 and 3 with a speed of 30 km/hour.

Thus, the correct answer is:

Between hours 1 and 2 (as this period falls within the faster segment of the overall speed increase).