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.