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A dog is sitting in the park, waiting for a cat, for 10 seconds. The dog sees a cat runs in the cat's direction at 10 m/s. The cat is 50 m away.
A dog is sitting in the park, waiting for a cat, for 10 seconds. The dog sees a cat runs in the cat's direction at 10 m/s. The cat is 50 m away. the cat begins running away as soon as the dog starts moving. Unfortunately for this particular cat is not faster than the dog. It's running speed is only 5 m/s. We will assume though that it reaches the speed instantaneously, while the dog must accelerate to its running speed of 10 m/s over a time of 2 seconds.
The dogs still catches the cat, because after two seconds it is running at 10 m/s while the cat is running at only 5 m/s. Thinking carefully, at the time the dog catches the cat, the distance the dog has traveled is larger than the distance the cat has traveled. How much larger?
Work out how much time the cat is running. Is that different from the time the dog is running? You will need to think about how far the cat has traveled and how far the dog has traveled at the time the dog catches the cat, which you worked out above. Explain reasoning.
Now, in the running cat scenario the dog must run further than if the cat was stationary because the cat is running away from the dog, adding extra distance. How much father does the dog run in the running Scenario than the dog ran if the cat was stationary?
