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From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is?
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From the velocity time graph shown in figure 8.8 the distance S travel...
Explanation:
A velocity time graph shows how an object's velocity changes over time. If an object is moving with uniform acceleration, the velocity time graph will be a straight line. The distance traveled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium OABC under the graph. This is because the area under the graph represents the distance traveled by the object.
Calculation of Area:
To calculate the area of the trapezium OABC, we need to first find the length of the two parallel sides. The parallel sides are OA and BC. The length of OA is the initial velocity of the object and the length of BC is the final velocity of the object. The time taken by the object to travel from initial velocity to final velocity is T. Hence, the length of BC can be calculated as BC = aT + OA.
Now, we can calculate the area of the trapezium OABC as follows:
Area of trapezium = (OA + BC) x T / 2
= (OA + aT + OA) x T / 2
= (2OA + aT) x T / 2
= (OA + (OA + aT)) x T / 2
= (initial velocity + final velocity) x T / 2
Hence, the distance traveled by the object in time T moving under uniform acceleration a is given by the formula:
Distance traveled = (initial velocity + final velocity) x T / 2
Conclusion:
The area under the velocity time graph represents the distance traveled by the object. For an object moving with uniform acceleration, the distance traveled can be calculated using the formula (initial velocity + final velocity) x T / 2, where T is the time taken by the object to travel from initial velocity to final velocity.
A velocity time graph shows how an object's velocity changes over time. If an object is moving with uniform acceleration, the velocity time graph will be a straight line. The distance traveled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium OABC under the graph. This is because the area under the graph represents the distance traveled by the object.
Calculation of Area:
To calculate the area of the trapezium OABC, we need to first find the length of the two parallel sides. The parallel sides are OA and BC. The length of OA is the initial velocity of the object and the length of BC is the final velocity of the object. The time taken by the object to travel from initial velocity to final velocity is T. Hence, the length of BC can be calculated as BC = aT + OA.
Now, we can calculate the area of the trapezium OABC as follows:
Area of trapezium = (OA + BC) x T / 2
= (OA + aT + OA) x T / 2
= (2OA + aT) x T / 2
= (OA + (OA + aT)) x T / 2
= (initial velocity + final velocity) x T / 2
Hence, the distance traveled by the object in time T moving under uniform acceleration a is given by the formula:
Distance traveled = (initial velocity + final velocity) x T / 2
Conclusion:
The area under the velocity time graph represents the distance traveled by the object. For an object moving with uniform acceleration, the distance traveled can be calculated using the formula (initial velocity + final velocity) x T / 2, where T is the time taken by the object to travel from initial velocity to final velocity.
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From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is?
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From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is?.
From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the velocity time graph shown in figure 8.8 the distance S travelled by the object in time T moving under uniform acceleration a is given by the area enclosed within the trapezium O ABC are under the graph .that is?.
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