Question

If you were shown two distance-time graphs that have different slopes, explain how you can tell which graph shows a faster speed.

a. The steeper slope indicates a faster speed.
b. The shallower slope indicates a faster speed.
c. Speed is independent of slope in distance-time graphs.
d. Time is the only factor determining speed in distance-time graphs.

Answer 1

(a): The steeper slope indicates a faster speed.

The steeper slope indicates a faster speed on a distance-time graph. A constant velocity is represented by a straight line with a constant slope, and a steeper graph indicates a faster moving object.

Step-by-step explanation:

To determine which distance-time graph shows a faster speed, you compare the slopes of the graphs. The correct answer is (a): The steeper slope indicates a faster speed. On a distance-time graph, the slope represents the velocity or speed of the object. Therefore, a steeper slope means that the distance is increasing more rapidly with respect to time, indicating a higher speed.

To know if the velocity is constant on a Distance vs. Time graph, you would look for a straight line with a constant slope. This would show that the velocity is constant over time. In contrast, for a car with a faster velocity, the Distance vs. Time graph would appear steeper compared to one with a slower velocity.

In summary, on a Distance vs. Time graph, the slope is equal to the velocity of the object. The steeper the slope, the greater the velocity, which means the object is moving faster. A straight line with a constant slope indicates a constant velocity.