Exploring Motion Down a Ramp: Understanding Velocity and Displacement

AI Thread Summary
The discussion centers on understanding the relationship between the area under the velocity-time graph and the displacement of a cart over a given time interval. It emphasizes that the area under the velocity-time graph represents the displacement of the cart, as displacement is the integral of velocity over time. Participants are encouraged to plot both displacement versus time and velocity versus time to visualize this relationship. The area under the curve of the velocity graph at a specific time t should equal the displacement x(t) at that same time. This connection is crucial for grasping the concepts of motion down a ramp.
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The question is `For the same time interval , how did the area beneath the velocity-time graph compare with the displacement of the cart? How should it compare?` I don't understand what they`re asking me to do, please help.
 
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Plot displacement (ordinate) vs time (abscissa), and velocity (ordinate) vs time (abscissa).

At some time t, what is the area under the curve of v(t) vs t, and how does that compare with the value of x(t) at the time t?
 

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