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.JEE Main 2023 (08 Apr Shift 2)ABoth Statement I and Statement II are trueBBoth Statement I and Statement II are falseCStatement I is correct but Statement II is falseDStatement I is incorrect but Statement II is true
Question
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.JEE Main 2023 (08 Apr Shift 2)ABoth Statement I and Statement II are trueBBoth Statement I and Statement II are falseCStatement I is correct but Statement II is falseDStatement I is incorrect but Statement II is true
Solution
The correct answer is A. Both Statement I and Statement II are true.
Here's why:
Statement I: The area under a velocity-time graph does indeed represent the distance travelled by an object in a given time. This is because the area under the graph is calculated by multiplying the time (x-axis) by the velocity (y-axis), which gives the distance.
Statement II: The area under an acceleration-time graph is equal to the change in velocity in the given time. This is because acceleration is defined as the rate of change of velocity with respect to time. Therefore, the integral (or area under the curve) of an acceleration-time graph gives the change in velocity.
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