What is the unit used to measure the quantity represented by the area under this graph?

Question

BlackTom AI · Accepted Answer

First, let's restate what the question is asking and what is given. The prompt asks: 'What is the unit used to measure the quantity represented by the area under this graph?' The graph shows velocity on the vertical axis (in m s^-1) and time on the horizontal axis (in s). Second, consider what the area under a velocity-time graph represents: the integral of velocity with respect to time gives displacement, which is a quantity measured in units of length. Since velocity has units of meters per second (m s^-1) and time has units of seconds (s), multiplying them (m s^-1 × s) leaves you with meters (m). Now, let's examine the options contextually. If the graph is a velocity-time plot, the area under it corresponds to distance traveled or displacement, not to a unit of velocity (m s^-1) or acceleration (m s^-2). Therefore, units that would be inconsistent include those that pair length with time inappropriately or those that describe rate-like quantities. At this point, note that the provided data lacks the listed answer options for evaluation. Nevertheless, the key concept remains: integrating velocity over time yields a length, so the appropriate unit is meters (m). Also keep in mind that if the graph represented speed instead of velocity, the interpretation is the same for the magnitude, since speed is non-directional but still measured in m s^-1 and its area under the curve still yields a length unit when integrated over time. The missing option list means we cannot compare each alternative, but the fundamental relationship between velocity units and time units leads to meters as the resulting unit for the area under a velocity-time curve. If there were options such as seconds (s), meters per second (m s^-1), or meters per second squared (m s^-2), you could immediately identify which one matches the derived unit for displacement, which is meters (m).

What is the unit used to measure the quantity represented by the area under this graph?

View Explanation

Log in for full answers

Similar Questions

The speed-time graphs for three vehicles X, Y, and Z are shown. If x, y, and z are the distance travelled by X, Y, and Z respectively in 8 s, which of the following comparison is correct?

The graph shows the speed of a can travelling along a conveyor belt in a factory. The can's displacement (in metres) can be calculated from the area under this graph. What is it?

The graph shows the speed of a remote controlled toy speed boat on a river. It speeds up for six seconds and then slows down for the same amount of time. The boat's displacement (in metres) can be calculated from the area under this graph. What is it?

The graph shows the speed of a remote controlled toy car on a pathway. It speeds up for one and a half seconds and then slows down for the same amount of time. The car's displacement (in metres) can be calculated from the area under this graph. What is it? Give your answer to 3 significant figures.

An object's movement is depicted by the following motion graph. [NOT DRAWN TO SCALE]The particle travels a distance of 251.1 m during the motion Find the maximum velocity, v, of the particle given the following values.A : 5.1 sB : 17.2 sC : 26.5 s

Which line is decelerating? If you cannot view this image, click here.

Using the following position vs. time graph, determine the total distance traveled between points B and D. d = _ _ _ _ _ _ c m

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler