The Correct Answer and Explanation is:
Of course. Based on the clearest part of the image, question (a), here are the correct answers and the detailed explanation.
Correct Answers for Question (a):
- The initial position of the object is 10 meters.
- The velocity of the object is 5 meters per second.
Explanation
The image displays a position versus time graph, which is a fundamental tool in physics for describing an object’s motion. The vertical axis, or y-axis, represents the object’s position in meters (m), while the horizontal axis, or x-axis, represents the passage of time in seconds (s).
To find the initial position, we need to determine the object’s location when the time is zero. This is the point where the graphed line intersects the vertical axis. Looking at the graph for question (a), the line begins at the point where time is 0 seconds. At this point, its value on the position axis is 10 meters. Therefore, the object’s starting or initial position is 10 meters from the origin.
To find the velocity, we need to calculate the slope of the line on the position versus time graph. The slope represents the rate of change of position, which is the definition of velocity. The formula for the slope is the “rise” divided by the “run”, or the change in position divided by the change in time.
We can calculate this by picking two distinct points on the line.
- Let’s use the starting point: (time = 0 s, position = 10 m).
- Let’s pick another clear point on the line, for instance, where time is 4 seconds. At this point, the position is 30 meters: (time = 4 s, position = 30 m).
Now, we apply the slope formula:
Velocity = (Change in Position) / (Change in Time)
Velocity = (Final Position – Initial Position) / (Final Time – Initial Time)
Velocity = (30 m – 10 m) / (4 s – 0 s)
Velocity = 20 m / 4 s
Velocity = 5 m/s
Since the line on the graph is straight, it indicates that the velocity is constant. The object is not speeding up or slowing down; it is moving steadily away from the origin at a rate of 5 meters for every second that passes.
