Multiple choice

A particle starts from east and travels a distance $S$ with uniform acceleration, then it travels a distance $2S$ with uniform speed, finally it travels a distance $3S$ with uniform retardation and comes to rest. If the complete motion of the particle is a straight line then the ratio of its average to maximum velocity is:

  1. $\displaystyle \dfrac{6}{7}$
  2. $\displaystyle \dfrac{4}{5}$
  3. $\displaystyle \dfrac{3}{5}$
  4. $\displaystyle \dfrac{2}{5}$
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C Correct answer
Explanation

The motion consists of three phases: acceleration, constant speed, and retardation. By calculating the time taken for each phase in terms of maximum velocity v, the total distance and total time are found to be 6S and 10S/v respectively. The average velocity is total distance divided by total time, which simplifies to 0.6v, or 3/5 of the maximum velocity.

AI explanation

Using the kinematic equations for uniformly accelerated motion, the time for the first phase is 2S/v, the second phase is 2S/v, and the third phase is 6S/v, making the total time 10S/v. The average velocity is the total displacement 6S divided by the total time 10S/v, which equals 3v/5. The maximum velocity is v, so the ratio of average velocity to maximum velocity is 3/5.

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