Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uni - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f . Let α be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time:

Solution & Step-by-step Explanation

Velocity of first particle: v_{1} = (u, 0) (assuming it moves along x-axis). Velocity of second particle at time t : v_{2} = (f t cos α, f t sin α) . Relative velocity v_{re l} = v_{2} - v_{1} = (f t cos α - u, f t sin α) . Magnitude squared V^{2} = (f t cos α - u)^{2} + (f t sin α)^{2} $ V^{2} = f^{2} t^{2} cos^{2} α + u^{2} - 2 u f t cos α + f^{2} t^{2} sin^{2} α $ V^{2} = f^{2} t^{2} + u^{2} - 2 u f t cos α To find least velocity, differentiate w.r.t t and equate to 0: \frac{d ( V ^{2} )}{d t} = 2 f^{2} t - 2 u f cos α = 0 f^{2} t = u f cos α ⟹ t = \frac{u cos α}{f}

Try it yourself before checking the explanation above.

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f . Let α be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time:

\frac{u s i n α}{f}

\frac{f c o s α}{u}

u sin α

\frac{u c o s α}{f}

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