The graph shows the velocity, in feet per second, of a decelerating car after the driver applies

step 1 Okay, we're going to go ahead and solve this problem. Now, first I want to note that because thi

The graph shows the velocity, in feet per second, of a...

Key Concepts

Area Under the Curve

The area under a velocity-time graph represents the displacement or distance traveled by the object. By calculating this area, typically through geometric shapes or integration, one can determine the total distance an object has moved over a specific time interval, even when the object is decelerating or accelerating.

Deceleration

Deceleration refers to the process of slowing down, where the magnitude of velocity decreases over time. In a velocity-time graph, deceleration is depicted by a downward slope, indicating that the object is reducing its speed until it possibly comes to a stop. This concept is key in understanding how velocity changes affect distance traveled.

Velocity-Time Graph

A velocity-time graph is a visual representation of an object’s velocity as it changes over time. The horizontal axis represents time, while the vertical axis represents velocity. In the context of motion analysis, the shape of the graph reveals important aspects of the object's movement, such as periods of constant velocity, acceleration, or deceleration.

Transcript

00:01 Okay, we're going to go ahead and solve this problem.

00:05 Now, first i want to note that because this is an estimation problem without using any precise values given from the graph, the answers are going to vary slightly between individuals and how you can do it.

00:20 So i am going to provide two possible solutions that most people might try to do.

00:26 Okay? so the most straightforward way to estimate the area, under the curve here is to see that this is sort of a triangular shape.

00:36 So if you connect the vertices like that, you can see that this is going to be quite of an overestimate, but we're going to be able to calculate the area of that triangle as an upper bound.

00:53 So let's calculate the area of that triangle right there.

00:57 You can see that the height is equal to 85.

01:02 You can see that the horizontal distance is equal to to 5.

01:08 So to calculate the area, it's a triangle, so it's one half base times height.

01:19 And this becomes 212 .5.

01:27 So that's one possible answer that you could do.

01:31 Another thing that i particularly did here is that looking at their grids, 2 .30 seems to be a legitimate point.

01:42 So what i was able to do is to say that, all right, this portion gives you a trapezoid, and this portion gives you a triangle, which seems like it's going to be a much closer approximation.

01:59 Again, it's still going to be an overestimate because this graph, the true graph, is concave up...

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