A rat and a cat is 35 m apart. When the rat started to run at 2 km/h (0.556 m/s), the cat started to chase him at 1 m/s2. Can the cat catch the rat in 10 seconds?

Compare (a/2)t^2 and 35 + 0.556 t.

Set them equal to find the time that the cat catches the rat.

To determine if the cat can catch the rat in 10 seconds, we need to analyze their respective speeds and distances.

Let's calculate the distance the rat will cover in 10 seconds at a speed of 0.556 m/s:

Distance = Speed × Time
Distance = 0.556 m/s × 10 s
Distance = 5.56 meters

Now, let's analyze the cat's acceleration. The cat's starting speed is 0 m/s, and it has an acceleration of 1 m/s^2. Using the equation:

Distance = Initial Speed × Time + 0.5 × Acceleration × Time^2

We can calculate the distance the cat will cover in 10 seconds:

Distance = 0 × 10 seconds + 0.5 × 1 m/s^2 × (10 seconds)^2
Distance = 0 + 0.5 × 1 m/s^2 × 100 seconds^2
Distance = 0 + 0.5 × 1 m/s^2 × 100 s^2
Distance = 0 + 0.5 m/s^2 × 100 m
Distance = 0 + 50 meters
Distance = 50 meters

From the calculations, we can see that the rat will cover a distance of 5.56 meters in 10 seconds, while the cat will cover a distance of 50 meters in the same duration.

As the rat is only 35 meters away from the cat initially, it is clear that the cat will be able to catch the rat within 10 seconds since it will cover a greater distance than the rat in that timeframe.