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In a particular time, the total distance travelled by the body is equal to
- a)the area which v vs t graph encloses with displacement axis
- b)the area which x vs t graph encloses with the time axis
- c)the area which v vs t graph encloses with time axis
- d)the area which a vs t graph encloses with axis
Correct answer is option 'C'. Can you explain this answer?
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In a particular time, the total distance travelled by the body is equa...
The total distance traveled by a body is indeed equal to the area under the velocity vs time graph with respect to the time axis (option c). This is because the area under the velocity vs time graph represents the total displacement, and the total distance traveled can be obtained by taking the absolute value of the displacement.
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In a particular time, the total distance travelled by the body is equa...
The correct answer is option 'C' - the area which the v vs t graph encloses with the time axis.
Explanation:
- **Understanding the v vs t graph**:
- In a velocity vs time (v vs t) graph, the velocity of an object is plotted against time. The slope of the graph represents the acceleration of the object.
- **Calculating distance traveled**:
- To calculate the total distance traveled by the body, we look at the area under the v vs t graph.
- Since distance is the integral of velocity with respect to time, the area under the v vs t graph gives us the total distance traveled by the body.
- **Why not other options**:
- Option 'A' talks about the area enclosed by the v vs t graph with the displacement axis. This area represents the change in displacement, not the total distance traveled.
- Option 'B' refers to the area enclosed by the x vs t graph with the time axis. This area represents displacement, not total distance.
- Option 'D' mentions the area under the a vs t graph. This area represents the change in velocity, not the total distance traveled.
- **Implications**:
- By understanding and analyzing the v vs t graph and the relationship between velocity, time, acceleration, and distance, we can accurately calculate the total distance traveled by a body in a given time period.
- **Conclusion**:
- Therefore, the total distance traveled by a body can be determined by looking at the area under the v vs t graph with the time axis. This method helps in accurately calculating the distance covered by the body during its motion.
Explanation:
- **Understanding the v vs t graph**:
- In a velocity vs time (v vs t) graph, the velocity of an object is plotted against time. The slope of the graph represents the acceleration of the object.
- **Calculating distance traveled**:
- To calculate the total distance traveled by the body, we look at the area under the v vs t graph.
- Since distance is the integral of velocity with respect to time, the area under the v vs t graph gives us the total distance traveled by the body.
- **Why not other options**:
- Option 'A' talks about the area enclosed by the v vs t graph with the displacement axis. This area represents the change in displacement, not the total distance traveled.
- Option 'B' refers to the area enclosed by the x vs t graph with the time axis. This area represents displacement, not total distance.
- Option 'D' mentions the area under the a vs t graph. This area represents the change in velocity, not the total distance traveled.
- **Implications**:
- By understanding and analyzing the v vs t graph and the relationship between velocity, time, acceleration, and distance, we can accurately calculate the total distance traveled by a body in a given time period.
- **Conclusion**:
- Therefore, the total distance traveled by a body can be determined by looking at the area under the v vs t graph with the time axis. This method helps in accurately calculating the distance covered by the body during its motion.
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In a particular time, the total distance travelled by the body is equal toa)the area which v vs t graph encloses with displacement axisb)the area which x vs t graph encloses with the time axisc)the area which v vs t graph encloses with time axisd)the area which a vs t graph encloses with axisCorrect answer is option 'C'. Can you explain this answer?
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