A horse canters away from its trainer in a straight line, moving 100 m away in 19.0 s. It then turns abruptly and gallops halfway back in 5.4 s.
(a) Calculate its average speed.
b) Calculate its average velocity for the entire trip, using "away from the trainer" as the positive direction.
To calculate the average speed, we need to divide the total distance traveled by the total time taken. The average velocity, on the other hand, takes into account the direction of motion.
a) Average Speed:
The horse moves 100 m away from its trainer in 19.0 seconds and then moves halfway back in 5.4 seconds. To calculate the total distance traveled, we add the distances:
Total distance = Distance away from trainer + Distance back to trainer
= 100 m + (100 m / 2)
= 100 m + 50 m
= 150 m
To calculate the average speed, we divide the total distance by the total time:
Average Speed = Total distance / Total time
= 150 m / (19.0 s + 5.4 s)
= 150 m / 24.4 s
≈ 6.15 m/s
Therefore, the average speed of the horse is approximately 6.15 m/s.
b) Average Velocity:
To calculate the average velocity, we need to account for the direction of motion. Since the horse is moving away from the trainer, we will consider "away from the trainer" as the positive direction.
The horse moves 100 m away from the trainer and then moves halfway back, which means it moves back 50 m in the opposite direction. The net displacement is the vector sum of these two movements:
Net Displacement = 100 m - 50 m
= 50 m
Since the horse moves back to the starting point, the net displacement is positive 50 m (in the chosen positive direction).
To calculate average velocity, we divide the net displacement by the total time:
Average Velocity = Net Displacement / Total time
= 50 m / (19.0 s + 5.4 s)
= 50 m / 24.4 s
≈ 2.05 m/s
Therefore, the average velocity of the horse, considering "away from the trainer" as the positive direction, is approximately 2.05 m/s.