JEE Main 2023 · 8 April · evening · Single correct · +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.
- (a) Both Statement I and Statement II are False.
- (b) Both Statement I and Statement II are true.
- (c) Statement I is incorrect but Statement II is true.
- (d) Statement I is correct but Statement II is false.
Answer and solution
Answer (c) Statement I is incorrect but Statement II is true.
Solution
Physics sir · 4 steps
Area under a velocity graph counts with sign, so it gives displacement, not distance.
- Velocity time area. Since v = dx/dt, the area under the v–t graph is ∫ v dt = Δ x, the displacement. Area below the time axis counts as negative.
- Why not distance. If the body turns back, the negative area cancels part of the positive area. Distance needs ∫ |v| dt, the total area with every part taken as positive. So Statement I is false in general.
∫_(t₁)^(t₂) a dt = ∫_(t₁)^(t₂) dv/dt dt = v₂ - v₁
- Acceleration time area. Since a = dv/dt, the signed area under the a–t graph is exactly the change in velocity. Statement II is true.
- So. Statement I is incorrect and Statement II is true, which is option (c).
The idea to keep. Signed area under a rate graph gives the change in the quantity: v–t gives displacement, a–t gives change in velocity. For distance, add up all areas as positive.
Answer from the NTA final answer key. Solution by PrepWiser.