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JEE Main 20254 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Evening Shift
Subject
Physics
Chapter
Motion in One Dimension

JEE Main 2025 · 4 April · Evening Shift · Physics · Motion in One Dimension

The displacement x versus time graph is shown below. (A) The...

The displacement x versus time graph is shown below.
The displacement x versus time graph is shown below. (A) The average velocity during 0 to 3 s is 10 ~m / s (B) The
(A) The average velocity during 0 to 3 s is 10 m/s10 \mathrm{~m} / \mathrm{s}
(B) The average velocity during 3 to 5 s is 0 m/s0 \mathrm{~m} / \mathrm{s}
(C) The instantaneous velocity at t=2 s\mathrm{t}=2 \mathrm{~s} is 5 m/s5 \mathrm{~m} / \mathrm{s}
(D) The average velocity during 5 to 7 s and instantaneous velocity at t=6.5 s\mathrm{t}=6.5 \mathrm{~s} are equal
(E) The average velocity from t=0t=0 to t=9 st=9 \mathrm{~s} is zero
Choose the correct answer from the options given below:

Options

  1. A(A), (D), (E) only
  2. B(B), (C), (D) only
  3. C(B), (D), (E) only
  4. D(B), (C), (E) only

Correct answer

D. (B), (C), (E) only

Step-by-step solution

<br/>⟨v→⟩=Δs→Δt=Sf−Sitf−tiv→=dsdt= slope <br/>\begin{aligned}<br/>& \langle\overrightarrow{\mathrm{v}}\rangle=\frac{\Delta \overrightarrow{\mathrm{s}}}{\Delta \mathrm{t}}=\frac{\mathrm{S}_{\mathrm{f}}-\mathrm{S}_{\mathrm{i}}}{\mathrm{t}_{\mathrm{f}}-\mathrm{t}_{\mathrm{i}}} \\ & \overrightarrow{\mathrm{v}}=\frac{\mathrm{ds}}{\mathrm{dt}}=\text{ slope }<br/>\end{aligned}
(A) 0 to 3sec;⟨v→⟩=5−03=5/3 m/s3 \mathrm{sec} ;\langle\overrightarrow{\mathrm{v}}\rangle=\frac{5-0}{3}=5 / 3 \mathrm{~m} / \mathrm{s}
(B) 0 to 5sec;⟨v⃗⟩=5−52=05 \mathrm{sec} ;\langle\vec{v}\rangle=\frac{5-5}{2}=0
(C) t=2;\mathrm{t}=2 ; slope =v⃗=5 m/s=\vec{v}=5 \mathrm{~m} / \mathrm{s}
(D) t=5\mathfrak{t}=5 to 7sec;⟨v→⟩=0−52=−2.5 m/s7 \mathrm{sec} ;\langle\overrightarrow{\mathrm{v}}\rangle=\frac{0-5}{2}=-2.5 \mathrm{~m} / \mathrm{s}
At t=6.5sec;v⃗=10t=6.5 \mathrm{sec} ; \vec{v}=10
(E) t=0\mathrm{t}=0 to t=9;⟨v→⟩=0\mathrm{t}=9 ;\langle\overrightarrow{\mathrm{v}}\rangle=0
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