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

Understanding the mean velocity of an object involves determining the central tendency of its motion in a specific direction. Let's look at how to calculate mean velocity in the context of our exercise. The mean velocity is computed by summing the product of each velocity and the number of cars travelling at that velocity in the eastward direction, and then subtracting the similar sum for the westward direction, due to their opposite movement relative to east.
In simple terms, if we consider eastward direction as positive, then we give westward direction a negative sign and perform the calculations accordingly. Once the total is obtained, it's divided by the total number of cars, giving us the mean velocity.
This concept is essential as it reflects the average velocity of the entire group of cars, considering the directions they are moving in. It's a vector quantity, which means it has both a magnitude and a direction, vital for understanding motion in physics.

Mean speed, on the other hand, is all about how fast the cars are moving, without considering their direction of travel. This value is scalar, which means it only has magnitude. To find the mean speed, we sum the products of the absolute values of velocities and the corresponding number of cars. This sum is then divided by the total number of cars, which gives the average speed of all cars regardless of their direction.
In our exercise, the absolute values are used since the direction is irrelevant for speed. Calculating mean speed is useful for understanding the general pace of a group of moving objects but lacks directionality information, unlike mean velocity.

In physics, speed and velocity are distinct concepts often interpreted together to understand an object's motion. Speed is a scalar quantity that refers to how fast an object is moving. It is calculated as the total distance traveled divided by the total time taken and has no direction associated with it.
Velocity, however, is a vector quantity. It describes the rate of change of an object's position and includes information about the direction of the movement. To calculate velocity, the displacement (distance in a straight line in a specific direction) is divided by the time taken. Since the mean velocity takes direction into account, it can sometimes result in a value of zero, especially if the motion is back and forth in equal amounts. This would never occur with speed, as it only concerns how much ground an object has covered over time without directionality.