In 6 secs, the dog covers- S=vt 8.9*6 = 53.4 m. In the same time, the cat covers, 53.4-3.8 = 49.6 m. Thus, speed of the cat, v= s/t, = 49.6/6 = 8.267 m/s
The cat was running at a constant speed of 8.27 m/s to evade the dog, as calculated by taking into account the dog's speed of 8.9 m/s, the cat's head start of 3.8 meters, and the time of 6.0 seconds.
To determine the speed at which the cat was running, we need to apply concepts of relative motion in a straight line, specifically using the equations for constant speed. The dog catches up to the cat after traveling for 6.0 seconds at a speed of 8.9 m/s. Since the cat had a head start of 3.8 meters, we can find the distance the dog had to cover to catch the cat, and then calculate the speed of the cat during these 6.0 seconds.
First, we find the distance the dog covers to catch the cat:
Distance dog covers = Speed of dog × Time
Distance dog covers = 8.9 m/s × 6.0 s = 53.4 m
The cat's total distance covered when the dog catches up includes both the head start and the distance the cat ran during the 6.0 seconds:
Total distance cat covers = Head start + Distance cat runs
Total distance cat covers = 3.8 m + (Speed of cat × Time)
Therefore, the distance the cat runs = Total distance dog covers - Head start
Distance cat runs = 53.4 m - 3.8 m = 49.6 m
Now, we can calculate the speed of the cat:
Speed of cat = Distance cat runs / Time
Speed of cat = 49.6 m / 6.0 s = 8.27 m/s
Thus, the cat was running at a constant speed of 8.27 m/s to evade the dog.
The speed of the cat is approximately 8.27 m/s. This is calculated by determining the distance the cat traveled in 6 seconds after considering its head start. Using the dog’s speed and the time taken to catch the cat allowed us to find this speed.
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