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Assertion (A): When the displacement of a body is directly proportional to the square of the time. Then the body is moving with uniform acceleration.
Reason (R): The slope of velocity-time graph with time axis gives acceleration.
Reason (R): The slope of velocity-time graph with time axis gives acceleration.
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true but R is not the correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Assertion (A): When the displacement of a body is directly proportiona...
Explanation:
Assertion (A): When the displacement of a body is directly proportional to the square of the time. Then the body is moving with uniform acceleration.
Reason (R): The slope of velocity-time graph with time axis gives acceleration.
Conclusion:
Both A and R are true but R is not the correct explanation of A.
To determine the correctness of the assertion and the reason, let's analyze each statement separately:
Assertion (A): When the displacement of a body is directly proportional to the square of the time. Then the body is moving with uniform acceleration.
This statement implies that the displacement-time relationship is given by:
s ∝ t^2
If displacement is directly proportional to the square of time, it means that the body is undergoing uniform acceleration. This is because the equation of motion for an object moving with uniform acceleration is given by:
s = ut + (1/2)at^2
Since the displacement is directly proportional to the square of time, the coefficient of t^2 is (1/2)a, which means the acceleration is constant. Therefore, assertion (A) is true.
Reason (R): The slope of velocity-time graph with time axis gives acceleration.
The slope of a velocity-time graph represents the rate of change of velocity with respect to time, which is acceleration. This is derived from the definition of acceleration as the rate of change of velocity:
a = Δv / Δt
The slope of the velocity-time graph is given by:
slope = (change in velocity) / (change in time)
Therefore, the reason (R) is true.
Conclusion:
From the analysis of both the assertion and the reason, we can conclude that:
Both A and R are true but R is not the correct explanation of A.
The reason (R) is true and provides additional evidence for the validity of the assertion (A), but it does not directly explain why the body is moving with uniform acceleration when the displacement is proportional to the square of time.
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Assertion (A): When the displacement of a body is directly proportiona...
Explanation:
The assertion (A) states that when the displacement of a body is directly proportional to the square of the time, then the body is moving with uniform acceleration. The reason (R) states that the slope of the velocity-time graph with the time axis gives acceleration.
Uniform Acceleration:
Uniform acceleration refers to a situation where the velocity of an object changes by the same amount in each equal interval of time. In other words, the rate of change of velocity is constant.
Displacement-Time Relationship:
If the displacement of a body is directly proportional to the square of the time, it can be expressed mathematically as:
S ∝ t²
Where S represents displacement and t represents time.
If we differentiate the above equation with respect to time, we get:
v = 2t
Where v represents velocity.
Therefore, the velocity of the body is directly proportional to time. This implies that the body is moving with uniform acceleration.
Velocity-Time Relationship:
The reason (R) states that the slope of the velocity-time graph with the time axis gives acceleration.
The velocity-time graph represents the change in velocity of an object with respect to time. The slope of this graph represents the rate of change of velocity, which is the acceleration.
If the velocity-time graph is a straight line, the acceleration is constant, indicating uniform acceleration. The slope of this straight line gives the value of acceleration.
Conclusion:
Both the assertion (A) and the reason (R) are true. The body is moving with uniform acceleration when the displacement is directly proportional to the square of the time. The reason correctly explains why this is the case, as the slope of the velocity-time graph gives the acceleration. Therefore, option B, "Both A and R are true but R is not the correct explanation of A," is the correct answer.
The assertion (A) states that when the displacement of a body is directly proportional to the square of the time, then the body is moving with uniform acceleration. The reason (R) states that the slope of the velocity-time graph with the time axis gives acceleration.
Uniform Acceleration:
Uniform acceleration refers to a situation where the velocity of an object changes by the same amount in each equal interval of time. In other words, the rate of change of velocity is constant.
Displacement-Time Relationship:
If the displacement of a body is directly proportional to the square of the time, it can be expressed mathematically as:
S ∝ t²
Where S represents displacement and t represents time.
If we differentiate the above equation with respect to time, we get:
v = 2t
Where v represents velocity.
Therefore, the velocity of the body is directly proportional to time. This implies that the body is moving with uniform acceleration.
Velocity-Time Relationship:
The reason (R) states that the slope of the velocity-time graph with the time axis gives acceleration.
The velocity-time graph represents the change in velocity of an object with respect to time. The slope of this graph represents the rate of change of velocity, which is the acceleration.
If the velocity-time graph is a straight line, the acceleration is constant, indicating uniform acceleration. The slope of this straight line gives the value of acceleration.
Conclusion:
Both the assertion (A) and the reason (R) are true. The body is moving with uniform acceleration when the displacement is directly proportional to the square of the time. The reason correctly explains why this is the case, as the slope of the velocity-time graph gives the acceleration. Therefore, option B, "Both A and R are true but R is not the correct explanation of A," is the correct answer.
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Assertion (A): When the displacement of a body is directly proportional to the square of the time. Then the body is moving with uniform acceleration.Reason (R): The slope of velocity-time graph with time axis gives acceleration.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer?
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ample number of questions to practice Assertion (A): When the displacement of a body is directly proportional to the square of the time. Then the body is moving with uniform acceleration.Reason (R): The slope of velocity-time graph with time axis gives acceleration.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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