[orgo814]

Cars were timed by police radar as they passed in both directions below a bridge. Their velocities (kilometers per hour, number of cars in parentheses) to the east and west were as follows: 80 E (40), 85 E (62), 90 E (53), 95 E (12), 100 E (2); 80 W (38), 85 W (59), 90 W (50), 95 W (10), 100 W (2). Wat are a) the mean velocity  b) the mean speed  c) the root mean square speed

I understand the formula would be 1/N (all of the numbers in parentheses) multiplied by the summation of velocities x cars in parentheses. For the root square speed, I would need to do 1/N^.5 multiplied by (summation of velocities^2 x number of cars in parentheses)^1/2.

However, isn't velocity the same thing as speed? I'm assuming the west and east have to do with something but I'm not sure. Help appreciated

[sjb]

Cars were timed by police radar as they passed in both directions below a bridge. Their velocities (kilometers per hour, number of cars in parentheses) to the east and west were as follows: 80 E (40), 85 E (62), 90 E (53), 95 E (12), 100 E (2); 80 W (38), 85 W (59), 90 W (50), 95 W (10), 100 W (2). Wat are a) the mean velocity  b) the mean speed  c) the root mean square speed

I understand the formula would be 1/N (all of the numbers in parentheses) multiplied by the summation of velocities x cars in parentheses. For the root square speed, I would need to do 1/N^.5 multiplied by (summation of velocities^2 x number of cars in parentheses)^1/2.

However, isn't velocity the same thing as speed? I'm assuming the west and east have to do with something but I'm not sure. Help appreciated

Velocity has a direction. So, if you had 1 car travelling at 10 miles per hour north, and another 10 miles an hour south, the mean velocity is 0, but the mean speed is 10 miles per hour

[orgo814]

So, for the mean speed I'll include all of them (east and west) in my calculation. For velocity, I should calculate the east as one component and the west as another and then add the two components?

[Corribus]

You have to use vector-think.  Assign the E-W axis to the X axis.  Call east the positive direction, west the negative direction.  So all cars going east are positive values, all going west are negative values.  Take an average.  Done.  (The sign will tell you whether the average is toward the east or west.)