Multiple choice

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

  1. $\dfrac{3}{8}ms^{-1}$
  2. $\dfrac{8}{3}ms^{-1}$
  3. $\dfrac{4}{3}ms^{-1}$
  4. $\dfrac{16}{3}ms^{-1}$
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B Correct answer
AI explanation

Let the total distance be 2x, so the first half distance is x and takes a time of x/2 seconds. The remaining distance x is covered in two equal time intervals t with speeds of 3 m/s and 5 m/s, giving 3t + 5t = x, which means t = x/8 and the total time for this second half is 2t = x/4 seconds. Using the average speed formula of total distance divided by total time, we get 2x divided by (x/2 + x/4). This simplifies to 2x divided by 3x/4, resulting in an average speed of 8/3 m/s.

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