Relative Velocity of Two Moving Bodies – Rankers Physics
Topic: Kinematics
Subtopic: Relative Motion in One Dimension

Relative Velocity of Two Moving Bodies

Two bodies are moving such that their (x)-coordinates are changing according to the law, \( X_1 = -3 + 2t + t^2 \) and \( X_2 = 7 - 8t + t^2 \). The relative speed (V) of bodies at the time of their meeting will be :
\(25 \text{ m/s}\)
\(15\text{ m/s}\)
\(5\text{ m/s}\)
\(10\text{ m/s} \)

Solution:

For meeting, equate positions: \(X_1 = X_2  -3 + 2t + t^2 = 7 - 8t + t^2;  10t = 10; t = 1 \text{ s} \). Differentiating positions gives velocities: \(v_1 = 2+2t = 4\text{ m/s}\) and \(v_2 = -8+2t = -6\text{ m/s}\) at \(t=1\text{ s}\). Relative speed \(V = |v_1 - v_2| = 10 \text {m/s}\).

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