Choose the best velocity-versus-time graph below for the air- plane (Figure P3.92).

Name: Problem 92, Chapter 3: College Physics
Uploaded: 2020-05-27T20:59:05-08:00
Duration: 5 min 2 s
Channel: Alexander Allen
Description: Choose the best velocity-versus-time graph below for the air- plane (Figure P3.92).

Choose the best velocity-versus-time graph below for the...

Key Concepts

Graph Interpretation

Interpreting a velocity-time graph involves analyzing both the slope and the area under the curve. The slope at any point reflects the object's instant acceleration, while the area between the graph and the time-axis represents the displacement of the object. This concept is essential for correctly choosing the graph that best represents an object’s motion in problems involving kinematics.

Velocity-Time Graph

A velocity-time graph illustrates how an object’s velocity changes over a period of time. The horizontal axis represents time, while the vertical axis shows velocity. The shape and slope of the graph directly indicate the motion of the object: a straight, horizontal line represents constant velocity, while a line with an upward or downward slope indicates acceleration or deceleration, respectively.

Acceleration

Acceleration is the rate at which an object's velocity changes with time. On a velocity-time graph, acceleration is depicted by the slope of the line. A constant slope indicates constant acceleration, and a changing slope or curvature indicates variable acceleration. Understanding acceleration is crucial for interpreting how an object’s speed is increasing or decreasing.

Transcript

00:01 Okay, question 92, what in a series of passage problems regarding a professor who has essentially hung a pendulum from a bulb, and he's using it to test the acceleration of an airplane.

00:17 We have the bulb acting like that.

00:19 The tension is keeping us fixed to a point, and the weight of the bulb acts down mg, with a measured angle here.

00:26 And in the previous questions, we've established the greater that angle, the greater the acceleration.

00:31 And we got a series of tabled answers.

00:34 Always a positive acceleration.

00:38 Basically, the idea was that if our acceleration is related to our angle, then a greater angle would lead to a greater acceleration.

00:50 And we got a consistent number of high accelerations, started out a little bit lower, became higher, and then tailed off quite quickly to become lower and lower.

00:59 These are the angles, sorry, and they led to the ability.

01:02 Appropriate information with the accelerations.

01:06 And you can of course take a look at the actual question themselves with the appropriate reading information.

01:13 But we're given a choice of four graphs to model the velocity time situation that is going on here.

01:21 And i'm just going to draw the axes out.

01:24 I'm going to talk through which graph best models the situation.

01:32 So just so we're all on the same page, we have a, and d and i'm going to draw on exactly what the figure shows us.

01:46 One has a horizontal line going like this, the other has a diagonal line like this, third a vertical line like this, and the fourth is a line like this.

02:01 Okay, so this is all about take -off speed of course our plane is taking off.

02:06 But talking this through there's some logic that we can take from this situation and that is if we just examine some of the information from the actual table itself, let's just take a few values.

02:19 So if we take some values of theta and some values of t.

02:22 So for example, at t seconds you are at zero, then you have 9 .9 degrees...

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