Question

select the correct location on the image. the lines on the position-time graph show the velocities of different vehicles. which line represents a vehicle moving at constant velocity?

Explanation:

Step1: Recall position - time graph concept

In a position - time graph, the velocity of an object is given by the slope of the graph, i.e., \(v=\frac{\Delta y}{\Delta x}\) (where \(y\) is position and \(x\) is time). For an object moving with constant velocity, the slope of the position - time graph should be constant. A constant slope means that the graph is a straight line (since the slope of a straight line is constant). Curved lines have a changing slope (so velocity is changing), and horizontal lines have a slope of 0 (object at rest), and straight non - horizontal lines have a constant slope.

Step2: Analyze each line

• The blue curve: It is a curve, so its slope (velocity) is changing.
• The horizontal line: Its slope is 0 (object is at rest, not moving with constant non - zero velocity or even zero velocity is a special case, but we are looking for constant velocity motion, and a horizontal line means velocity \(v = 0\) (constant but at rest). But among the straight lines:
• The straight lines (the non - curved ones): The straight lines have a constant slope. So the straight lines (the ones that are not curved) represent motion with constant velocity. From the graph, the straight lines (for example, the one passing through the origin and the one with negative slope and the horizontal one) have constant slopes. But the question is to identify which line. The key is that a straight line in a position - time graph represents constant velocity (since slope = velocity is constant). So the straight lines (the non - curved lines) are the ones with constant velocity. Looking at the graph, the straight lines (like the one from the origin, the one with negative slope, and the horizontal one) have constant slopes. The curved line has a changing slope (so changing velocity). So the correct line is the straight line (any of the straight lines, but typically the ones with non - zero slope or zero slope but straight). In the given graph, the straight lines (the ones that are not the blue curve) have constant velocity. For example, the line that is a straight line (not curved) has a constant slope, so it represents constant velocity.

Answer:

The straight - line (the non - curved line, e.g., the one passing through the origin or the other straight lines) represents a vehicle moving at constant velocity. In the graph, the straight lines (excluding the curved blue line) have a constant slope, so they represent constant velocity motion.