explain in your own word why is it acceptable to take displacements of the trolleys x1 and x2 as a measure of the velocities of the trolleys.
How do you expect us to "explain in your own words"?
Oh, boy, here we go! So, you're asking why it's okay to take the displacements of the trolleys, let's call them x1 and x2, and use them as a measure of their velocities, huh? Well, let me put on my clown hat and break it down for you!
Okay, picture this: You're sitting on a roller coaster, and you're moving through different positions, right? Now, if you wanna know how fast you're zooming through the air, you'd probably look at the distance you've covered over time, right? Same idea here! In this case, x1 and x2 represent the displacement, or the distance, the trolleys have traveled from their starting points.
Now, by looking at how far these trolleys have moved, we can get an idea of how fast they're going! If the displacements are increasing quickly, that means they're zooming along like a coked-up cheetah. But if the displacements aren't changing much, it means they're moving slower, like a tortoise on tranquilizers.
Of course, we're oversimplifying things a bit, because there's more to velocity than just displacement. But taking the displacements as a measure of velocity can give us a good estimate of how fast those trolleys are chugging along. So, while it's not exactly perfect, it's acceptable and can help us understand what's going on with those trolleys!
Hope that explanation tickled your funny bone!
It is acceptable to take the displacements of the trolleys, denoted as x1 and x2, as a measure of their velocities because displacement and velocity are closely related concepts in physics.
Displacement refers to the change in position of an object from its initial position to its final position. In the context of trolleys, the displacements x1 and x2 would represent how far the trolleys have moved from their respective initial positions.
Velocity, on the other hand, is a measure of how fast an object's position changes with time. It is calculated as the rate of change of displacement over time. Mathematically, velocity (v) is equal to displacement (Δx) divided by the time interval (Δt): v = Δx/Δt.
If the displacements x1 and x2 are being measured over a fixed time interval, then the ratio Δx1/Δt would provide an estimation of the average velocity of trolley 1, and similarly, Δx2/Δt would provide an estimation of the average velocity of trolley 2.
While this method provides an estimation of the average velocity, it assumes a constant velocity and does not capture any fluctuations or changes in velocity that may occur during that time interval. However, for many practical situations where the time interval is small and fluctuations are negligible, using displacements as a measure of velocities can be a reasonable approximation.
It is acceptable to take displacements of the trolleys x1 and x2 as a measure of their velocities because displacement is directly related to velocity. In physics, velocity is the rate at which an object changes its position, and it includes both the magnitude (speed) and direction. Displacement, on the other hand, measures the change in position of an object from its initial point to its final point, taking into account both magnitude and direction.
When we consider the displacements of the trolleys x1 and x2, we are specifically looking at how far they have moved from their original positions. By observing the change in their positions over a given time period, we can determine their velocities.
Mathematically, velocity is defined as the derivative of displacement with respect to time. By differentiating the displacement function with respect to time, we can find the instantaneous rate of change in position, which gives us the velocity. This is known as the first derivative of displacement with respect to time.
Therefore, by analyzing the displacements of the trolleys x1 and x2 and applying calculus principles, we can obtain their velocities. Taking the displacements as a measure of velocity allows us to understand how fast and in what direction the trolleys are moving relative to their initial positions.