How can u determine that a falling object has reached terminal velocity from a velocity time graph of its motion?
u can determine if a falling object has reached terminal velocity from a velocity-time graph of its motion by its stop of acceleration. The falling object no longer accelerates and travels at constant velocity. At this point, the upward forces equal the downward forces.
Explain how u would determine the distance the object travelled. How does ur answer differ from ur answer to a? (I do not get this question) wouldn't u times the v by time to get distance?
If you have a velocity versus time graph, the distance traveled is the area under that velocity curve. For every little vertical slice of the graph from the time axis up to the velocity curve the little area around that vertical line is velocity times that little time, which is distance. When you add all those slices up you get the area which is the total distance.
thanks for the explanation Damon, it was very helpful:) thanks so much:)
You are welcome. Congratulations on solving your first calculus problem :)
Oh, I see what you're saying! It seems like you're asking how to determine the distance the object has traveled using the velocity-time graph. Well, the distance can be found by calculating the area under the velocity-time graph. You would integrate the velocity function over time. So yes, you're correct, you would multiply the average velocity by the time interval to get the distance traveled.
As for the difference between this answer and the previous one, the first answer was about determining if the object had reached terminal velocity, while this answer is about calculating the distance traveled. They're two different aspects. Does that clear things up for you?
To determine the distance traveled by the falling object, you can use the area under the velocity-time graph. Since velocity is the rate of change of displacement, the area under the graph represents the total displacement of the object during the specified time interval.
To calculate the distance traveled, you would indeed multiply the velocity by the time. However, it's important to note that this formula works only for a constant velocity scenario. You can use this formula when the falling object has reached terminal velocity and is moving at a constant speed. At this point, velocity remains constant, so multiplying velocity by time will provide an accurate measure of the distance traveled.
On the other hand, if we are considering the entire motion of the falling object, including the initial acceleration phase before reaching terminal velocity, the distance traveled cannot be determined simply by multiplying the velocity by time. In this case, you would need to consider the changing acceleration and calculate the total distance traveled using more advanced mathematical techniques, such as integrating the area under the velocity-time graph.