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KCET2009PhysicsMotion in One Dimension

A body of mass m moving along a straight line covers half the distance with a speed of 2 ~ms ⁻¹ . The remaining half of the distance is covered in two equal time intervals with a speed of 3 ~ms ⁻¹ and 5 ~ms ⁻¹ respectively. The average speed of the particle for the entire journey is

Options

  1. A3 8 ~ms ⁻¹
  2. B8 3 ~ms ⁻¹
  3. C4 3 ~ms ⁻¹
  4. D16 3 ~ms ⁻¹

Correct answer

B. 8 3 ~ms ⁻¹

Step-by-step solution

Let the total distance travelled by the body is 2 S . If t ₁ is the time taken by the body to travel first half of the distance, then t ₁= S 2 Let t ₂ be the time taken by the body for each time interval for the remaining half journey. S =3 t ₂+5 t ₂=8 t ₂ So, average speed = Total distance travelled Total time taken = 2 S t₁+2 t₂ = 2 S S 2 + S 4 = 8 3 ~ms ⁻¹

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