Question

a student investigates the motion of a toy vehicle. the student graphs 40 seconds of data from the investigation. motion of a toy vehicle which statement best describes the motion of the toy vehicle during the first 30 seconds of the investigation?

Explanation:

To determine the motion of the toy vehicle during the first 30 seconds, we analyze the distance - time graph:

Step 1: Recall the meaning of the slope in a distance - time graph

In a distance - time graph, the slope of the line is given by the formula \(slope=\frac{\text{change in distance}}{\text{change in time}}\). And the slope of the distance - time graph represents the speed of the object, where \(speed = \frac{\text{distance}}{\text{time}}\).

Step 2: Analyze the graph for the first 30 seconds

For the first 30 seconds, the graph is a straight line. A straight - line segment in a distance - time graph implies that the slope (and thus the speed) is constant.
If we consider two points on the line, say at \(t = 0\) seconds, the distance \(d=0\) meters and at \(t = 30\) seconds, let's assume the distance is \(d = 12\) meters (from the graph's trend). The speed \(v=\frac{\Delta d}{\Delta t}=\frac{12 - 0}{30-0}=\frac{12}{30} = 0.4\) m/s (the actual value depends on the exact scale, but the key is that the slope is constant). A constant slope in a distance - time graph means that the object is moving at a constant speed (uniform motion).

So, the toy vehicle moves at a constant speed during the first 30 seconds. If we were to choose from common options (even though they are not provided here), the correct description would be related to the vehicle moving with a constant speed (uniform motion) as the distance - time graph is a straight line for the first 30 seconds.

Answer:

To determine the motion of the toy vehicle during the first 30 seconds, we analyze the distance - time graph:

Step 1: Recall the meaning of the slope in a distance - time graph

In a distance - time graph, the slope of the line is given by the formula \(slope=\frac{\text{change in distance}}{\text{change in time}}\). And the slope of the distance - time graph represents the speed of the object, where \(speed = \frac{\text{distance}}{\text{time}}\).

Step 2: Analyze the graph for the first 30 seconds

For the first 30 seconds, the graph is a straight line. A straight - line segment in a distance - time graph implies that the slope (and thus the speed) is constant.
If we consider two points on the line, say at \(t = 0\) seconds, the distance \(d=0\) meters and at \(t = 30\) seconds, let's assume the distance is \(d = 12\) meters (from the graph's trend). The speed \(v=\frac{\Delta d}{\Delta t}=\frac{12 - 0}{30-0}=\frac{12}{30} = 0.4\) m/s (the actual value depends on the exact scale, but the key is that the slope is constant). A constant slope in a distance - time graph means that the object is moving at a constant speed (uniform motion).

So, the toy vehicle moves at a constant speed during the first 30 seconds. If we were to choose from common options (even though they are not provided here), the correct description would be related to the vehicle moving with a constant speed (uniform motion) as the distance - time graph is a straight line for the first 30 seconds.