1) On a plot of position x versus time t for an object’s motion, what corresponds to the object’s velocity at any given instant t1?
A. slope at the point on the plot corresponding to t1
B. intercept on the horizontal axis
C. inverse of the slope at the point on the plot corresponding to t1
D. intercept on the vertical axis
2) On a plot of position x versus time t for an object’s motion, what corresponds to the object’s average velocity between instant t1 and instant t2?
A. inverse of the slope of a line connecting the corresponding points on the plot
B. intercept of the plot on the vertical axis
C. intercept of the plot on the horizontal axis
D. slope of a line connecting the corresponding points on the plot
For Number 2, I think the answer is D. But I am not sure. Could you please provide an explanation to your answer? I really want to understand this concept.
Slope at the point on the plot corresponding to t1
For question number 1, the correct answer is A. The slope at the point on the plot corresponding to t1 corresponds to the object's velocity at that instant. In a position-time graph, the slope of the line at any given point represents the rate at which the object is changing its position.
For question number 2, the correct answer is D. The average velocity between instant t1 and instant t2 can be determined by calculating the slope of the line connecting the corresponding points on the plot. The slope represents the change in position divided by the change in time, which is precisely the definition of average velocity.
To better understand these concepts, it is helpful to consider the physical interpretation of slope and its relation to velocity. The slope of a line represents the ratio of the vertical distance covered (position) to the horizontal distance covered (time), commonly known as the rate of change. In the context of motion, this rate of change is equivalent to velocity. So, by calculating the slope or rate of change between two points on a position-time graph, you can determine the object's average velocity over that time interval.
For question 1, the correct answer is A. The slope of the line at any given point on the plot corresponds to the object's velocity at that instant. To understand why this is the case, let's consider the definition of velocity.
Velocity is defined as the rate of change of position over time. In calculus terms, it is the derivative of the position function with respect to time.
So, if you have a plot of position versus time, the slope of the line at any given point represents the rate of change of position with respect to time at that particular instant. This rate of change is precisely the definition of velocity.
Therefore, option A, which states that the slope at the point on the plot corresponding to t1 corresponds to the object's velocity at that instant, is the correct answer.
Now, let's move on to question 2.
For question 2, the correct answer is D. The slope of a line connecting the corresponding points on the plot represents the average velocity between those two instants, t1 and t2. Let's break it down.
Average velocity is defined as the total change in position divided by the total change in time. In terms of the plot, this can be visualized as a line connecting the positions at t1 and t2.
The slope of this line, which is calculated by taking the change in position (y-axis) divided by the change in time (x-axis), gives us the average velocity between t1 and t2.
Therefore, option D, which states that the slope of a line connecting the corresponding points on the plot corresponds to the object's average velocity between t1 and t2, is indeed the correct answer.
Understanding the concepts of slope and the relationship between position, velocity, and their graphical representations is crucial in physics. I hope this explanation helps you in grasping these concepts better. Let me know if you have any further questions!