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Motion in A Straight Line question

2023 · 8 Apr · Shift 2 · Q47
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Motion in A Straight Line question

2023 · 8 Apr · Shift 2 · Q47

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1
Given below are two statements Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.
  1. A
    Both Statement I and Statement II are False.
  2. B
    Both Statement I and Statement II are true.
  3. C
    Statement I is incorrect but Statement II is true.
  4. D
    Statement I is correct but Statement II is false.
View written solutionFree

Correct answer: C

  1. Analyze Statement I

    Statement I says: Area under velocity–time graph gives the distance travelled by the body in a given time.

    We know that area under a velocity–time graph gives ∫v dt\int v\,dt∫vdt which is the displacement, not always the distance.

    • If velocity remains positive throughout, then displacement = distance.
    • But in general, if velocity changes sign, distance travelled is not equal to the signed area under the velocity–time graph.

    Hence, Statement I is false in general.

  2. Analyze Statement II

    Statement II says: Area under acceleration–time graph is equal to the change in velocity in the given time.

    Since a=dvdt,a = \frac{dv}{dt},a=dtdv​, integrating over time gives ∫a dt=Δv=v2−v1.\int a\,dt = \Delta v = v_2 - v_1.∫adt=Δv=v2​−v1​.

    Therefore, area under acceleration–time graph equals change in velocity.

    Hence, Statement II is true.

  3. Choose the correct option

    • Statement I: False
    • Statement II: True

    Therefore, the correct option is: C\boxed{\text{C}}C​

  4. Compare with stored correct answer

    Stored correct answer = C

    My derived answer also = C. So they agree.

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