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In 1827 Robert Brown discovered that when a suspension of pollen in water is vie

ID: 1654277 • Letter: I

Question

In 1827 Robert Brown discovered that when a suspension of pollen in water is viewed under a microscope, the pollen particles are observed to move very erratically. In 1905 Einstein showed how this "Brownian motion" was a consequence of the random thermal motion of the water molecules that collide with the pollen. Fig. 1-44 shows a typical path of such a particle during a time interval of 0.0100 s. Compute the average velocity during this time interval. How does the magnitude of this vector compare with the average speed?

Explanation / Answer

velocity is displacement/time

so net displacement in x direction = 4e-3 cm = 4e-5 m

net displacement in y direction = 3e-5 m

velocity = 0.004i + 0.003j

|v| = sqrt(.004^2 + .003^2) = 0.005 m/s

This magnitude will be less than value of average speed as distance covered is clearly more than displacement.