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

Question

BlackTom AI · Accepted Answer

Area under a speed–time graph represents displacement (or distance if speed is non‑negative). Units are obtained by multiplying the vertical axis unit (speed, m s^-1) by the horizontal axis unit (time, s), giving metres.

1. Relevant knowledge points and concepts
- The shaded quantity is the area under a speed (vertical) vs time (horizontal) graph.
- Area under a rate vs time curve equals the accumulated quantity (integral): here, speed integrated over time = displacement.
- Units of an integral are the product of the integrand’s units and the differential variable’s units.

2. Step-by-step reasoning
- Read the axis labels: speed has units m s^-1 (m/s) and time has units s.
- The area calculation is essentially ∫ speed dt.
- Unit analysis: (m s^-1) × (s) = m.

3. Intermediate unit calculation
- Write units algebraically: m s^-1 · s = m · (s/s) = m (since s cancels).
- Thus the resulting unit is metres.

4. Why the correct answer is correct
- Integrating a velocity or speed over time accumulates length (distance/displacement). The dimensional analysis shows the product of speed and time yields length (metres), so option a. m is correct.

5. Why the other options are incorrect
- b. m/s^2 is units of acceleration (rate of change of velocity), not an integrated area of speed vs time.
- c. m/s is the unit of speed/velocity (the graph’s vertical axis), not the area under the curve.
- d. s is the unit of time (the horizontal axis), not the product from area calculation.

6. Conclusion
- The unit for the quantity represented by the shaded area is metres, confirming the correct answer is a. m.

What is the unit used to measure the quantity represented by the area under this graph?单项选择题

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