Question

Jesse represents his speed on a graph, where y represents distance in miles and x represents time in hours. If the graph shows a straight line with a slope of 60 miles per hour, what does it represent?

a) Jesse's constant speed.
b) Jesse's acceleration.
c) Jesse's changing speed.
d) Jesse's position.

Answer 1

The straight-line graph with a slope of 60 miles per hour indicates that Jesse maintains a constant speed of 60 miles per hour. So the correct answer is (a) Jesse's constant speed.

Step-by-step explanation:

The given graph represents a straight line with a slope of 60 miles per hour. A straight line on a distance-time graph with a constant slope indicates constant speed. In this case, the slope of 60 miles per hour signifies that Jesse is moving at a constant speed of 60 miles per hour.

To understand this, we can use the formula for the slope of a line:

slope = change in y / change in x

In this context, the change in distance
`(\( \Delta y \))` is the vertical change on the graph, and the change in time
`(\( \Delta x \))` is the horizontal change. Since the slope is given as 60 miles per hour, it means for every 1-hour increase in time, there is a corresponding 60-mile increase in distance. This consistent ratio indicates a constant speed.

Therefore, option (a) Jesse's constant speed is the correct interpretation of the graph. It implies that Jesse is maintaining a steady pace of 60 miles per hour throughout the time represented on the graph.

Options (b) Jesse's acceleration, (c) Jesse's changing speed, and (d) Jesse's position are not applicable because the graph shows a straight line with a constant slope, indicating constant speed rather than changes in acceleration, varying speed, or position.So the correct answer is (a) Jesse's constant speed.

Answer 2

a) Jesse's constant speed because Jesse's motion is constant as depicted by the straight line with a slope of 60 miles per hour on the distance-time graph.

Step-by-step explanation:

The graph displaying a straight line with a slope of 60 miles per hour indicates a constant speed for Jesse. The slope of a distance-time graph represents the speed, and a straight line signifies a consistent rate of change in distance over time.

Therefore, Jesse's motion is characterized by a constant speed throughout the represented time frame. In a distance-time graph, the slope represents the speed or rate of change in distance per unit of time.

When the line is straight, as in this case, it implies that the speed remains unchanged over time. A slope of 60 miles per hour indicates that for every hour that passes, Jesse covers a distance of 60 miles.

There's no variation or acceleration depicted in the graph; instead, it confirms a steady pace maintained by Jesse during the observed period. Acceleration is denoted by changes in speed over time, which would manifest as a curve or non-linear graph.

Jesse's changing speed or position would result in a curved line on the graph, not a straight line with a constant slope. Therefore, the straight line with a slope of 60 miles per hour in Jesse's graph distinctly illustrates a scenario of steady and unchanging speed—a hallmark of constant motion in this context. Thus option a) is correct.