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Speed is the rate of change in position in a given amount of time. Thus, speed is measured in units of meters/second (m/s), kilometers per hour (km/hr) and more familiarly miles/hour (mph). Average speed is then the total distance traveled divided by the total time spent traveling.
Velocity has identical units to speed but the direction of motion must also be specified. In addition, velocity looks at the displacement (the shortest distance from the start of the motion to the end of the motion). This can lead to some interesting differences between average speed and average velocity.
Consider, for example, a runner on a 400 meter track. Suppose the runner completes exactly 4 laps in 6 minutes. Their average speed is then 1600 m/360 s or 4.44 m/s. However, there average velocity is zero! This is because their displacement is zero.
Another example would be if someone drives 300 m east, then 400 m north in a total time of 5 minutes. Their average speed is 700 m/300 s or 2.33 m/s. However, their displacement is 500 m from where they started. Therefore, their average velocity is 500 m/300 s or 1.67 m/s @ 53.13 degrees north of east.
The basic difference is that speed is a scalar quantity, and velocity is a vector quantity; basically, direction matters when talking about velocity, and it doesn't when we are talking about speed. Speed is how fast something is moving--the rate at which a distance is covered. Velocity measures how fast something changes position. Think of it this way: if you run 100 meters in 10 seconds then immediately run back to your starting point in 10 seconds, your average speed is 10 meters per second--you have covered 200 meters in 20 seconds. Your average velocity is zero--you haven't changed your position after 20 seconds.
Average velocity is a vector quantity, meaning it includes the magnitude and the direction of the object.
While average speed is a scalar quantity which only has the magnitude of the object.
Speed refers to the distance travelled by an object per unit of time. For example,
if a car travels 100 kilometers in one hour. Its average speed is 100 kmph. The usual unit of measurement of speed is kmph, or kilometers per hour. It is a scalar quantity, that is, only one component namely the distance covered is measured.
Velocity on the contrary refers to the rate of displacement with reference to a unit of time. It refers to how fast an object changes position. The unit of measurement of velocity is the same as that of speed, but its a derived unit. Velocity is a vector quantity, that is two components are measured - the distance covered and the direction.
The difference is speed does not depend on direction while velocity depends on direction. Speed is a scalar quantity while velocity is a vector quantity. Like this, if it is speed, you would just refer it to 2 m/s. If it is velocity, you refer it as this 2m/s east (with direction).
So, average speed is the total distance taken over the total time taken (regardless of direction) while average velocity is the same whole thing, except it includes direction.
It will be easier to understand the difference between average speed and average velocity by first understanding the difference between speed and velocity.
Speed of an object is defined as rate of change of position in a linear direction without consideration of the direction in which the object moves. In contract velocity refers to change of position in a specific linear direction. Thus a car moving at the speed of 80 kilometers per hours from north to south has the same speed as a car moving at the speed of 80 kilometers in south to north direction. However when consider velocity, if the velocity of first car above is 80 kilometers per hour, that of the second car will be -80 kilometers per hour.
Now coming to average speed and average velocity, the average speed is the total linear distance covered divided by the time taken to cover this distance. In contrast average velocity is the net displacement of an object in a given time divided by the time taken. Thus when a car travelling at speed 80 kilometers per hour travels in the north south direction for one hour and south north direction in next hour it covers a total linear distance of 160 kilometers in 2 hours. This gives an average speed of 80 kilometers per hour. Now considering velocity, we find that this car has reached, after travelling for two hours, the same point from which it had started. Thus there is no net displacement in its position. Therefore its average velocity is zero.
Suppose if the car had travelled at the speed of 80 kilometers per hour first in north south direction for 1 hour, and then in west east direction for 1 hour the net displacement would be:
= (80^2 + 80^2)^1/2 = 113.14 kilometers
in south west direction. In this case the average velocity will be:
113.14/2 = 56.57 kilometers per hour
in south west direction.
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