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Motion In Straight Line

Question
CBSEENPH11026320

The distance x (in µm) covered by a molecule starting from point A at time t = 0 and stopping at another point B in given by the equation  x = t2 2 - t3 The distance between A and B ( in μm) is closed to

  • 10.7

  • 20.7

  • 40.7

  • 50.7

Solution

A.

10.7

Given that distance

         x = t2 2 - t3

On differentiating

        dxdt = 4t - t2

For x to be maximum,

         dxdt = 0

⇒     4t - t2 = 0

⇒            t = 4

∴ Maximum distance

      xmax42  2 - 43 

              = 16 × 6 - 43

              = 16 × 23

    xmax = 10.7