Acceleration for Midpoint Meeting – Rankers Physics
Topic: Kinematics
Subtopic: Relative Motion in One Dimension

Acceleration for Midpoint Meeting

Two bodies separated by a distance of \('s'\) start moving towards each other with speeds of \(v\) and \(2v\) respectively. The uniform acceleration with which the first body should move so that they meet at the middle is:
\(\frac{v^2}{s}\)
\(\frac{v^2}{2s}\)
\(\frac{8v^2}{s}\)
\(\frac{4v^2}{s}\)

Solution:

The second body travels \(s/2\) at constant speed \(2v\) in time \(t = s/(4v)\). For the first body: \(s/2 = vt + \frac{1}{2}at^2\). Substituting \(t\) gives \(s/2 = s/4 + a s^2 / (32v^2)\), which simplifies to \(a = 8v^2/s\).

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