Relative motion in one dimension questions with solutions

Showing 1–10 of 66 questions

• NumericmediumKinematics part-3 Relative motionRelative motion in one dimension

  Two cars are 300 m apart and move directly towards each other with speeds 20 m/s and 30 m/s. They apply brakes simultaneously. Car A retards at 2 m/s² and car B at a m/s². They just avoid collision and both come to rest before reversing. If a=n/4 m/s², find n.

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• MCQmediumKinematics part-3 Relative motionRelative motion in one dimension

  Trains A and B have lengths l and 4l and enter a tunnel of length L from opposite directions with speeds 108 km h⁻¹ and 72 km h⁻¹. Train A takes 35 s less than B to cross the tunnel. Given L = 60l, the tunnel length is:

  Options

  • Option A

    2700 m

  • Option B

    1800 m

  • Option C

    1200 m

  • Option D

    900 m

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• MCQmediumKinematics part-3 Relative motionRelative motion in one dimension

  Two cars move in the same direction at 30 km h⁻¹ and are 5 km apart. A third car moving in the opposite direction meets them at an interval of 4 min. Find the speed of the third car.

  Options

  • Option A

    60 km h⁻¹

  • Option B

    5 km h⁻¹

  • Option C

    30 km h⁻¹

  • Option D

    45 km h⁻¹

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• MCQeasyKinematics part-3 Relative motionRelative motion in one dimension

  Object A moves at 10 m s⁻¹ and object B at 5 m s⁻¹ in the same positive x-direction. A is 100 m behind B. Time taken by A to catch B is:

  

  Options

  • Option A

    18 s

  • Option B

    16 s

  • Option C

    20 s

  • Option D

    17 s

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• MCQeasyKinematics part-3 Relative motionRelative motion in one dimension

  A boat travels a distance L downstream and then the same distance L upstream, returning to its starting point. Its speed relative to water is u and river speed is v, with u > v. The average velocity for the complete trip is:

  Options

  • Option A

    u

  • Option B

    (u² - v²)/u

  • Option C

    v

  • Option D

    0

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• MCQmediumKinematics part-3 Relative motionRelative motion in one dimension

  Cars A and B move on the same straight road in the same direction. At t=0, A is 120 m behind B. Their speeds are 30 m/s and 20 m/s respectively. From t=0, B accelerates uniformly at 2 m/s². What minimum constant acceleration must A have so that A just touches the limiting condition of overtaking B (minimum separation becomes zero)?

  Options

  • Option A

    29/12 m/s²

  • Option B

    5/2 m/s²

  • Option C

    8/3 m/s²

  • Option D

    3 m/s²

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• Multi-correctmediumKinematics part-3 Relative motionRelative motion in one dimension

  Train A moves due north at 54 km h⁻¹ and train B moves due south at 90 km h⁻¹ on parallel tracks. A monkey runs on the roof of train A at 18 km h⁻¹ relative to A, opposite to A's motion. Which statements are correct?

  Select all that apply

  • Option A

    Velocity of B relative to A is 144 km h⁻¹ due south.

  • Option B

    Velocity of ground relative to B is 90 km h⁻¹ due north.

  • Option C

    Velocity of the monkey relative to ground is 36 km h⁻¹ due north.

  • Option D

    Velocity of the monkey relative to B is 126 km h⁻¹ due north.

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• MCQmediumKinematics part-3 Relative motionRelative motion in one dimension

  A stone is dropped from rest from the top of a 45 m high tower. At the same instant, another stone is projected vertically upward from the ground with a speed of 30 m/s. Neglect air resistance and take g = 10 m/$s^2.$ After what time do the two stones meet?

  Options

  • Option A

    1 s

  • Option B

    1.5 s

  • Option C

    2 s

  • Option D

    2.5 s

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• Multi-correctmediumKinematics part-3 Relative motionRelative motion in one dimension

  Two point cars approach each other with constant speeds 12 m/s and 8 m/s from an initial separation of 200 m. A bird of speed 30 m/s starts from the first car, repeatedly flies to the other car and reverses instantaneously on reaching it. Which statements are correct?

  Select all that apply

  • Option A

    The cars meet after 10 s

  • Option B

    The bird travels a finite total distance of 300 m

  • Option C

    The bird completes infinitely many one-way flights before the cars meet in the idealized model

  • Option D

    The duration of every successive bird flight is the same

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• MCQmediumKinematics part-3 Relative motionRelative motion in one dimension

  Cars A and B move in the same direction with speeds Vₐ and Vᵦ, where Vₐ>Vᵦ. A is initially a distance s behind B and then applies brakes with uniform retardation a. Which condition ensures no collision?

  Options

  • Option A

    s < (Vₐ-Vᵦ)²/(2a)

  • Option B

    s = (Vₐ-Vᵦ)²/(2a)

  • Option C

    s ≥ (Vₐ-Vᵦ)²/(2a)

  • Option D

    s ≤ (Vₐ-Vᵦ)²/(2a)

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