A horse canters away from its trainer in a straight line, moving 140 m away in 16.0 s. It then turns abruptly and gallops halfway back in 5.0 s.
(a) Calculate its average speed.
(b) Calculate its average velocity for the entire trip, using "away from the trainer" as the positive direction.
(a) It travels a total of 210 m in 21 s. Ignore the fact that the direction changes. The average speed is 210/21 = 10 m/s.
(b) The net displacement is 70 m in 21 s. The average velocity is 70/21 = 3.33 m/s
To calculate the average speed of the horse, we need to divide the total distance traveled by the total time taken.
(a) Average speed = Total distance / Total time
In this case, the horse moves 140 m away from its trainer and then gallops halfway back, which is 70 m. So, the total distance traveled is 140 m + 70 m = 210 m.
The horse takes 16.0 s to move 140 m away and then 5.0 s to travel 70 m back. The total time taken is 16.0 s + 5.0 s = 21.0 s.
Therefore, the average speed of the horse is 210 m / 21.0 s = 10 m/s.
(b) Average velocity is different from average speed as it takes into account both the magnitude and direction of motion. To calculate average velocity, we divide the displacement by the total time taken.
Displacement is the shortest distance between the initial and final positions, considering the direction. In this case, both the initial and final positions are in the same straight line away from the trainer. Therefore, the magnitude of the displacement is 210 m (from part (a)).
The initial and final positions are in the positive direction (away from the trainer). So, the average velocity is also in the positive direction.
Average velocity = Displacement / Total time
Therefore, the average velocity of the horse for the entire trip is 210 m / 21.0 s = 10 m/s in the positive direction (away from the trainer).