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COMEDK2024Morning ShiftPhysicsMotion in One DimensionActual

When two objects are moving along a straight line in the same direction, the distance between them increases by 6 ~m in one second. If the objects move with their constant speed towards each other the distance decreases by 8 ~m in one second, then the speed of the objects are :

Options

  1. A14 ~ms ⁻¹ and 2 ~ms ⁻¹
  2. B7 ~ms ⁻¹ and 1 ~ms ⁻¹
  3. C3.5 ~ms ⁻¹ and 1 ~ms ⁻¹
  4. D3.5 ~ms ⁻¹ and 2 ~ms ⁻¹

Correct answer

B. 7 ~ms ⁻¹ and 1 ~ms ⁻¹

Step-by-step solution

Let the speeds of the two objects be v₁ and v₂ in ms ⁻¹ , where v₁ > v₂ . When moving in the same direction, the relative speed is v₁ - v₂ . The distance between them increases by 6 m in 1 s , so v₁ - v₂ = 6 m 1 s = 6 ms ⁻¹ . When moving towards each other, the relative speed is v₁ + v₂ . The distance between them decreases by 8 m in 1 s , so v₁ + v₂ = 8 m 1 s = 8 ms ⁻¹ . Adding the two equations: (v₁ - v₂) + (v₁ + v₂) = 6 + 8 2v₁ = 14 v₁ = 7 ms ⁻¹ . Subtracting the first equation from the second: (v₁ + v₂) - (v₁ -

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