Average Speed Vs. Average Velocity?

Question

Say a horse canters away from it's trainer in a straight line, moving 130.0 m away in 14.0 s. It then turns abruptly and gallops halfway back in 4.80 s. Use "away from the trainer" as the positive direction.
a] what is the average speed?
b] what is the average velocity?

I can't fully grasp the concept of the two, and also displacement...

Answer 1

Velocity is a vector quantity, whereas speed isn't.

What does that mean? Well, it means that velocity will be expressed as a rate + a direction, but speed will simply be expressed as a rate. This problem is a pretty good illustration of that ...

Let's start with speed. For the first part of the horse's travels, it moves 130.0 m in 14 s. Then it moves 65 m in 4.80 s. If we take these and add them, we find that the horse moved 195 m in 18.80 s. This means its average speed was 10.4 m/s.

Velocity:
We have the horse's movement initially as 130.0 in 14 s AWAY from the trainer. The horse then moves halfway back TOWARD the trainer. Since "away from the trainer is positive," then back toward the trainer is negative. This means we have to subtract.

130.0 - 65 = 65 m (positive because it only moved back half the distance).
14.0 + 4.8 = 18.8 s (time is added, not subtracted).

This gives us 65 m/18.8s, which means that the velocity is 3.5 m/s AWAY from the trainer.

As for displacement, the horse moved a total of 195 m, but its net displacement is only 65 m (since it moved back toward the trainer).

I hope this was helpful.

Answer 2

Average speed would be more useful because it measure the total distance the horse can cover over over time. Average velocity, however, would only be relative to a fixed point, so a horse going around a curve would have a different and smaller average velocity than the average speed, and it would less accurately reflect its abilities.

Answer 3

Speed is a scalar quantity. That means it measures the magnitude of something. Speed is how much distance one has traveled divided by the amount of time it took to do so. It does not matter which direction or one travels, only that one has traveled. 100 yards is a measure of distance. 100 yards per minute is a measure of speed. You could travel 50 yards forward and 50 yards back to the starting point, and you still have traveled 100 yards distance and thus has a non-zero speed.

Velocity is a vector quantity. That means it measures the magnitude of something as well as the direction of that magnitude. It is how much displacement one has traveled divided by the amount of time it took to do so. Displacement is a vector quantity. Displacement also is described by a magnitude and a direction. 100 yards to the north is a measure of displacement. 100 yards per minute to the north is a measure of velocity. If you travel 50 yards to the north and then travel 50 yards south to the starting point, yout displacement is zero. Hence your velocity is also zero, despite the fact that you walked 100 yards.

So to answer your question:

(a) the average speed is how much distance the horse traveled divided by total time it took to do so. The total distance is 130 m+130/2 m=195 m. The time it took to do so is 14.0 s + 4.8 s = 18.8 s. The average speed is 195 m/ 18.8 s = 10.4 m/s.

(b) the average velocity is how much displacement the horse traveled divided by total time it took to do so. The total displacement is 130 m - 130/2 m = 65 m using the sign convention that away from trainer is positive direction. The total time it took to do so is the same 18.8 s. The average velocity is 65 m / 18.8 s = 3.46 m/s away from the trainer.

Answer 4

Average velocity is the straight-line distance from start to finish, divided by the elapsed time. If you end up where you started, the average velocity is zero.

Average speed is the length of the path followed, divided by the elapsed time. If the path is curved, you have to add up all the little straight piece of it to get the length of the path.