A cat is being chased by a dog. Both are running in a straight line at constant speeds. The cat has a head start of 3.3 m. The dog is running with a speed of 9.0 m/s and catches the cat after 6.7 s. How fast did the cat run?

I see that the velocity and time are given, so does that mean that i have to solve for the acceleration?

50

To solve for the speed at which the cat ran, we need to use the concept of relative motion. Since both the cat and the dog are running in a straight line at different speeds, we can imagine being at a fixed point and observing their motion. In this case, let's consider the frame of reference of the dog.

Given:
- Dog's speed: 9.0 m/s
- Time taken for the dog to catch the cat: 6.7 s
- Cat's head start: 3.3 m

To find the cat's speed, we can first calculate the distance covered by the dog during the time it takes to catch the cat.

Distance covered by the dog = Dog's speed * Time taken
= 9.0 m/s * 6.7 s
≈ 60.3 m

Now, since the dog catches the cat after running for 6.7 seconds, the total distance covered by the cat would be the distance covered by the dog plus the head start distance of the cat.

Total distance covered by the cat = Distance covered by the dog + Cat's head start
= 60.3 m + 3.3 m
= 63.6 m

Since we know the time and distance covered by the cat, we can calculate the cat's speed using the formula:

Speed = Distance / Time
= 63.6 m / 6.7 s
≈ 9.49 m/s

So, the cat ran at a speed of approximately 9.49 m/s to be caught by the dog after 6.7 seconds.