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NTA Abhyas JEE Main2020PhysicsMotion in One DimensionPractice

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by X P t = a t + b t 2 and X Q t = f t - t 2 . At what time do the cars have the same velocity?

Options

  1. Aa - f 1 + b
  2. Ba + f 2 b - 1
  3. Ca + f 2 1 + b
  4. Df - a 2 1 + b

Correct answer

D. f - a 2 1 + b

Step-by-step solution

v P = d x P d t = a + 2 b t v Q = d x Q d t = f - 2 t v P = v Q ⇒ a + 2 b t = f - 2 t 2 t + 2 b t = f - a ⇒ t = f − a 2 ( b + 1 )

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