A dog runs 150{\rm m} away from its master in a straight line in 8.4{\rm s} , and then runs halfway back in one-third the time.Calculate its average speed,average velocity?
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To calculate the average speed of the dog, we need to determine the total distance traveled and divide it by the total time taken.
Let's break down the problem step by step:
1. Distance traveled in the first leg: The dog runs 150 m away from its master.
2. Time taken in the first leg: 8.4 s.
3. Distance traveled in the second leg: The dog runs halfway back, which means it travels half of 150 m, which is 75 m.
4. Time taken in the second leg: One-third of the time taken in the first leg, which is (1/3) * 8.4 s.
Now we can calculate the average speed:
Total distance traveled = Distance in the first leg + Distance in the second leg
= 150 m + 75 m
= 225 m
Total time taken = Time in the first leg + Time in the second leg
= 8.4 s + (1/3) * 8.4 s
= 8.4 s + 2.8 s
= 11.2 s
Average speed = Total distance traveled / Total time taken
= 225 m / 11.2 s
≈ 20.09 m/s
So, the average speed of the dog is approximately 20.09 m/s.
To calculate the average velocity, we need to consider the direction of the movement. Since the dog runs away from its master and then runs halfway back, the displacement is zero because the dog ends up at the same position as its master.
Average velocity = Displacement / Total time taken
Since the displacement is zero and the total time taken is 11.2 s, the average velocity of the dog is zero.
Therefore, the average speed of the dog is approximately 20.09 m/s, while the average velocity is zero.