The displacement x versus time graph is shown below. (A) The average velocity during 0 to 3 s is 10 m/s (B) The average velocity during 3 to 5 s is 0 m/s (C) The instantaneous velocity at t = 2 s is 5 m/s (D) The average velocity during 5 to 7 s and instantaneous velocity at t = 6.5 s are equal (E) The average velocity from t = 0 to t = 9 s is zero Choose the correct answer from the options given below: (a) (B), (C), (D) only (b) (B), (D), (E) only (c) (A), (D), (E) only (d) (B), (C), (E) only

Answer: (d). (A) v0→ 3 = (5 - 0)/(3) = 5/3 m/s, not 10. False. (B) x(3) = x(5) = 5 m, so v = 0. True. (C) At 2 s the body is on line AC: slope = (5 - (-5))/(3 - 1) = 5 m/s. True. (D) v5→ 7 = (0 - 5)/(2) = -2.5 m/s; at 6.5 s slope of EF = (0 - 10)/(1) = -10 m/s. Not equal. False. (E) x(9) = x(0) = 0, so v = 0. True. Correct: (B), (C), (E). So the answer is (d).

The displacement x versus time graph is shown below. (A) The average… | JEE Main 2025 (4 Apr, Shift 2)

Q8JEE Main 2025 · 4 APR · SHIFT 2Medium

Graphs of Motion

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is $10\text{ m/s}$

(B) The average velocity during 3 to 5 s is $0\text{ m/s}$

(D) The average velocity during 5 to 7 s and instantaneous velocity at $t = 6.5\text{ s}$ are equal (E) The average velocity from $t = 0$ to $t = 9\text{ s}$ is zero

Choose the correct answer from the options given below:

Show answer and solution

Answer: (d)

(A) $\bar v_{0\to 3} = \frac{5 - 0}{3} = \frac{5}{3}\text{ m/s}$ , not 10. False.
(B) $x(3) = x(5) = 5\text{ m}$ , so $\bar v = 0$ . True.
(C) At 2 s the body is on line AC: slope $= \frac{5 - (-5)}{3 - 1} = 5\text{ m/s}$ . True.
(D) $\bar v_{5\to 7} = \frac{0 - 5}{2} = -2.5\text{ m/s}$ ; at 6.5 s slope of EF $= \frac{0 - 10}{1} = -10\text{ m/s}$ . Not equal. False.
(E) $x(9) = x(0) = 0$ , so $\bar v = 0$ . True.
Correct: (B), (C), (E). So the answer is (d).

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