Question

A student is measuring and graphing the motion of a toy car. The car moves to the left

with constant velocity along the number line shown below.
-9-8-7-6-5-4-3
1 2 3 4 5 6
89
Which of these statements correctly describes the slope of the graph and the velocity when the student
constructs a position-time graph of the car's motion?
A student has selected the following for their answer choice.
The slope will be negative but the velocity will be positive.
Explain why this answer is incorrect in the speaker section of the presentation

Answer 1

The correct statement is: The slope will be negative, and the velocity will be negative.

Step-by-step explanation:

When constructing a position-time graph, the slope represents the velocity of the object. In this case, as the car is moving to the left along the number line, the position-time graph's slope will be negative.

This is because the car is experiencing a negative change in position over time, indicating a leftward direction. Since velocity is the rate of change of position, and the position change is negative (leftward), the velocity will also be negative.

To clarify, velocity is a vector quantity that includes both magnitude and direction. A negative slope in a position-time graph reflects a negative velocity, signifying motion in the opposite direction of the positive axis.

In this context, a negative velocity indicates that the car is moving to the left. Therefore, the student's initial choice of a negative slope and positive velocity is incorrect, as the direction of the car's motion is leftward, and velocity should align with the direction of motion.

In conclusion, the correct relationship between the slope of the position-time graph and the velocity for the toy car moving to the left is that both are negative. This is consistent with the car's leftward motion along the number line, emphasizing the importance of understanding the connection between graph slopes and physical quantities in the study of motion.