the fence posts around a large pasture are 2.5m apart. a horse starts running west beside the fence. when the horse passes the fifth fence post, your second hand is on the 9.0 mark. when the horse passes the fourteenth fence post, the second hand is on 11.5 seconds. what is the horse’s velocity?

Not sure how to do this at all. Can I please get help and can I get an explanation at each step and work as well? Thank you!

The time was measured at post 5 and post 14.

The number of post gaps between post 5 and post 9 is 14 - 5 = 9
We know each post gap is 2.5 m long.
So the horse ran 2.5 m x 9 = 22.5 m West
This displacement of the horse occurred in 11.5 s - 9 s = 2.5 s.
Velocity = displacement / time
= 22.5 m / 2.5 s = ____ m/s West

9.0 m/s west

Sure, I'd be happy to help you with this problem! But before we start, I must warn you that I'm a bot who uses humor to answer questions, so my explanations might not be entirely serious. Now, let's take a look at the problem:

First, let's calculate the time it took for the horse to pass the 5th fence post. We know that the horse covered a distance equal to 4 times the distance between the fence posts (since it passed 5 posts). So, the distance covered by the horse is 4 * 2.5m = 10m.

Next, we need to calculate the time taken by the horse to cover this distance. From the given information, we know that when the horse passes the 5th fence post, the second hand is on the 9.0 mark. This means that the horse took 9.0 seconds to cover the 10m distance.

Now, let's move on to the second part of the problem. We need to calculate the time it took for the horse to pass the 14th fence post. Again, the horse covered a distance equal to 13 times the distance between the fence posts (since it passed 14 posts). So, the distance covered is 13 * 2.5m = 32.5m.

From the information given, we know that when the horse passes the 14th fence post, the second hand is on the 11.5 seconds mark. This means that the horse took 11.5 seconds to cover the 32.5m distance.

Lastly, let's calculate the velocity of the horse. Velocity is defined as the distance traveled divided by the time taken. In this case, the horse covered a distance of 32.5m in a time of 11.5 seconds. So, the velocity of the horse is 32.5m/11.5s = 2.83m/s.

So, the horse's velocity is approximately 2.83 meters per second. I hope this helps!

To find the horse's velocity, we first need to determine the time it takes for the horse to pass each fence post.

Let's start by finding the time it takes for the horse to pass from the 5th fence post (P5) to the 14th fence post (P14).

The distance between P5 and P14 is given by:
Distance = (14 - 5) * 2.5m
Distance = 9 * 2.5m
Distance = 22.5m

The time it takes for the horse to cover this distance can be found using the formula:
Speed = Distance / Time

We need to calculate the time it takes for the horse to pass from P5 to P14, so we rearrange the formula to solve for Time:
Time = Distance / Speed

Now, let's calculate the time:
Time = 22.5m / 11.5s
Time ≈ 1.9565s

So, it takes the horse approximately 1.9565 seconds to pass from P5 to P14.

Now, let's find the horse's velocity. Since the horse runs in a straight line, and the distance between fence posts is constant, the horse's velocity will also be constant.

We can use the formula:
Velocity = Distance / Time

To find the distance the horse travels, we subtract the distance from the 5th fence post to the starting point from the distance between P5 and P14:
Distance = 22.5m - (5 * 2.5m)
Distance = 22.5m - 12.5m
Distance = 10m

Now, let's calculate the horse's velocity:
Velocity = 10m / 1.9565s
Velocity ≈ 5.1165 m/s

Therefore, the horse's velocity is approximately 5.1165 m/s in the west direction.

To find the horse's velocity, we can use the formula:

velocity = displacement / time

First, let's determine the displacement traveled by the horse. The distance between consecutive fence posts is 2.5m. Therefore, when the horse passes the fifth fence post, it has covered a total distance of 2.5m × 4 = 10m.

Next, we need to calculate the time taken by the horse to cover this displacement. From the question, we know that when the horse passes the fifth fence post, the second hand is on the 9.0 mark. This represents a time of 9.0 seconds.

So, the time taken to cover a displacement of 10m is 9.0 seconds. Now, we can find the horse's speed:

speed = displacement / time
speed = 10m / 9.0s ≈ 1.11 m/s

Therefore, the horse's velocity is approximately 1.11 m/s.