Motion in a Plane - JEE mains PYQ series part-1

 

Motion in a Plane — Quiz 1 (Questions 1–10)

Attempt Questions 1–10. MCQs use radio buttons; numeric questions accept keyboard input. Numeric answers have ±1% tolerance. Click Check to reveal the correct answer and a compact stepwise solution for that question.

Instructions

• MCQs — select one radio option.
• Numerical — type numeric value (no units). Use dot for decimals. ±1% accepted.
• Press Check below each question to reveal solution for that question.
• Use Check All & Score for full evaluation.

1. Position of an ant (S in metres) moving in Y–Z plane is given by S = (2 t) ŷ + (5 t^2) ẑ (here we interpret the pasted expression as S = 2t j + 5t² k). The magnitude and direction of velocity of the ant at t = 1 s will be: [27 Jan 2024 — Shift-I]

(a) 16 m/s in y-direction (b) 4 m/s in x-direction (c) 9 m/s in z-direction (d) 4 m/s in y-direction

2. A particle starts from origin at t=0 with velocity 5 î m/s and acceleration a = (3 î + 2 ĵ) m/s². When the x-coordinate becomes 84 m, the particle's speed is α m/s. The value of α is _______. [27 Jan 2024 — Shift-I]

3. Coordinates: x = 2 + 4t, y = 3t + 8t². The motion of the particle is: [04 Apr 2024 — Shift-I]

(a) Non-uniformly accelerated (b) Uniformly accelerated having motion along a straight line (c) Uniform motion along a straight line (d) Uniformly accelerated having motion along a parabolic path

4. A force F = (10 î + 5 ĵ) N acts on an object of mass 100 g. The position at t = 2 s starting from rest is (a î + b ĵ) m. The ratio a/b = ______. [25 June 2022 — Shift-I]

5. At t=0 a particle starts from height 7ẑ cm (z constant). Coordinates: x = 3t, y = 5t³. At t = 1 s, acceleration is: [28 July 2022 — Shift-II]

(a) −30 ĵ (b) 30 ĵ (c) 3 î + 15 ĵ (d) 3 î + 15 ĵ + 7 ẑ

6. Particle A: x(t) = 10 + 8t − 3t² along x-axis. Particle B: y(t) = 5 − 8t³ along y-axis. At t = 1 s, the speed of particle B as measured in the frame of particle A is v m/s. Find v (nearest reasonable precision). [08 Jan 2020 — Shift-I]

7. Particle starts at origin t=0 with initial velocity 3.0 î m/s, acceleration (6.0 î + 4.0 ĵ) m/s². When y = 32 m, the x-coordinate is D m. Find D. [09 Jan 2020 — Shift-II]

(a) 50 (b) 40 (c) 32 (d) 60

8. From origin at t=0 with initial velocity 5 ĵ m/s, a particle accelerates with a = (10 î + 4 ĵ) m/s². At time t its coordinates are (20 m, y₀ m). Find t and y₀. [04 Sept 2020 — Shift-I]

(a) 4 s and 52 m (b) 2 s and 24 m (c) 5 s and 25 m (d) 2 s and 18 m

9. A balloon moves up vertically above A. At height h₁ it is seen from B (distance d from A) at angle 45° with vertical. After climbing h₂ and the observer moves to C at distance 2.464 d from A, the balloon is seen at 60° with vertical. Find h₂ in terms of d. [05 Sept 2020 — Shift-I]

(a) d (b) 0.732 d (c) 1.464 d (d) 0.464 d

10. A particle moves with velocity v = K y î + x ĵ (K constant). The general equation of its path is: [09 Jan 2019 — Shift-I]

(a) y = x² + constant (b) y² = x + constant (c) y² = x² + constant (d) xy = constant