Question

motion graph analysis
a
b.
c
d.
e.
f.
descriptions of motion

1. acceleration
2. constant speed (high rate of speed)
3. constant speed (low rate of speed)
4. negative acceleration (deceleration)
5. no motion (stopped)
6. moving backwards (constant velocity in reverse)

graph a matches description _ because _
graph b matches description _ because _
graph c matches description _ because _
graph d matches description _ because _
graph e matches description _ because _
graph f matches description _ because _

Explanation:

Graph A

• Step1: Analyze the graph

The distance does not change over time. In a distance - time graph, if the distance is constant (\(d = k\), where \(k\) is a constant), the object is not moving.

Graph B

• Step1: Analyze the slope

The slope of a distance - time graph represents speed (\(v=\frac{\Delta d}{\Delta t}\)). A steep positive - sloped straight line in a distance - time graph indicates a high constant speed.

Graph C

• Step1: Analyze the slope

The slope of the distance - time graph is negative and constant. A negative slope in a distance - time graph means the object is moving in the reverse direction. But if we consider the motion in terms of acceleration (if we assume a non - velocity interpretation, in a non - standard sense, if we consider the rate of change of the slope in a more complex kinematic analysis, but more simply, if we assume a mis - labeled axis (if it was a velocity - time graph, but assuming it's a distance - time graph mis - related to the given descriptions), a negative slope in a distance - time graph for the given description set (where description 6 is moving backwards at constant velocity) is incorrect. However, if we consider the problem's description set and assume a mis - match in axis labels (if we consider it as a velocity - time graph in the context of the given descriptions), a negative slope in a velocity - time graph is deceleration.

Graph D

• Step1: Analyze the slope

The slope of the distance - time graph is increasing. The slope of a distance - time graph is velocity (\(v = \frac{\Delta d}{\Delta t}\)). If the slope (velocity) is increasing, the object is accelerating.

Graph E

• Step1: Analyze the slope

The slope of the distance - time graph is decreasing. If we assume a non - standard relation (if we consider it as a velocity - time graph mis - labeled as distance - time), a decreasing slope in a velocity - time graph is deceleration. But if we consider the given description set, there is no perfect match. However, if we assume a mis - categorization in the problem's design.

Graph F

• Step1: Analyze the slope

The slope of the distance - time graph is positive and small. The slope of a distance - time graph is velocity (\(v=\frac{\Delta d}{\Delta t}\)). A small positive slope indicates a low constant speed.

Answer:

Graph A: \(5\), because the distance does not change over time.
Graph B: \(2\), because it has a steep positive - sloped straight line (high constant speed).
Graph C: \(6\), because it has a negative - sloped straight line (moving backwards at constant velocity).
Graph D: \(1\), because its slope (velocity) is increasing.
Graph E: (No perfect match in the given description set, but if we assume a mis - categorization, no valid answer from 1 - 6 as per strict interpretation).
Graph F: \(3\), because it has a small positive - sloped straight line (low constant speed).