A horse canters away from its trainer in a straight line, moving 160 m away in 12.0 s. It then turns abruptly and gallops halfway back in 4.5 s.
(a) Calculate its average speed.m/s
(b) Calculate its average velocity for the entire trip, using "away from the trainer" as the positive direction. m/s
To calculate the average speed of the horse, we need to find the total distance traveled and divide it by the total time taken.
(a) To find the total distance traveled, we add the distances covered during the two parts of the motion.
In the first part, the horse moves 160 m away from the trainer.
In the second part, the horse turns around and gallops halfway back, which means it covers a distance of (160 m / 2) = 80 m.
Therefore, the total distance traveled by the horse is 160 m + 80 m = 240 m.
Now, we can calculate the average speed by dividing the total distance by the total time taken:
Average speed = Total distance / Total time
Average speed = 240 m / (12.0 s + 4.5 s)
Average speed = 240 m / 16.5 s
Average speed ≈ 14.54 m/s
So, the average speed of the horse is approximately 14.54 m/s.
(b) To calculate the average velocity, we need to consider the direction in which the horse is moving. In this case, "away from the trainer" is considered the positive direction.
In the first part of the motion, the horse moves away from the trainer, and in the second part, it moves towards the trainer. Since the horse returns halfway during the second part, we can consider the distance covered in both parts as equivalent.
Therefore, the total displacement of the horse is 160 m - 80 m = 80 m (positive direction).
Now, we can calculate the average velocity by dividing the total displacement by the total time taken:
Average velocity = Total displacement / Total time
Average velocity = 80 m / (12.0 s + 4.5 s)
Average velocity = 80 m / 16.5 s
Average velocity ≈ 4.85 m/s (in the positive direction)
So, the average velocity of the horse for the entire trip, considering "away from the trainer" as the positive direction, is approximately 4.85 m/s.