Question

If x = the amount of time passed in seconds, which function could represent horse?

Answer 1

The function representing the distance covered by a horse over time is
`\(d(x) = v \cdot x\)` , where
`\(d(x)\)` is the distance,
`\(v\)` is the speed, and
`\(x\)` is the time in seconds.

Step-by-step explanation:

In the given scenario, the relationship between time and distance for a horse is described by a simple linear function. The equation
`\( d(x) = v \cdot x \)` signifies that the distance covered
`(\( d(x) \))` is directly proportional to the time passed
`(\( x \))` , with the speed of the horse
`(\( v \))` being the constant of proportionality.

In this context, the constant
`\( v \)` represents the horse's speed, determining how many meters the horse can cover in one second. If the speed of the horse is, for example, 5 meters per second, the function becomes
`\( d(x) = 5x \),` indicating that the horse covers 5 meters for every second elapsed.

This linear relationship aligns with the basic principles of motion, where the distance covered by an object is equal to its speed multiplied by the time elapsed. In the context of a horse, this function accurately represents how its distance traveled changes with respect to time, providing a clear and concise mathematical model for the scenario described.