A particle starts from rest and moves with uniform acceleration in a straight line. It covers the first half of its total distance with an average velocity v₁ , and the second half of its total distance with an average velocity v₂ . The ratio v₂ v₁ is equal to:

Step-by-step solution

Let the total distance be 2d and the uniform acceleration be a . The velocity of the particle at the start is u = 0 . Using the third equation of motion, v^2 = u^2 + 2as , the velocity at the midpoint (distance d ) is v' = 2ad . The velocity at the end of the journey (distance 2d ) is v'' = 2a(2d) = 2 ad . For uniformly accelerated motion, the average velocity over any interval is the arithmetic mean of the initial and final velocities for that interval. Average velocity for the first half, v₁ = 0 + 2ad 2 . Average