Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In

Chameleons catch insects with their tongues, which they can...

Key Concepts

Unit Conversion

Ensuring that all units, such as time, distance, and acceleration, are consistent is crucial for correct calculations in physics. Converting units (for example, milliseconds to seconds) is a fundamental step when applying kinematic equations.

Piecewise Analysis in Kinematics

This refers to breaking down a motion into separate segments or phases that may have different kinematic behaviors, such as an accelerated phase followed by a constant velocity phase. Analyzing each phase independently and then combining the results helps accurately determine overall displacement.

Uniformly Accelerated Motion

This concept deals with motion where an object's acceleration remains constant. It is characterized by equations relating displacement, initial velocity, acceleration, and time, such as the equation d = (1/2)at². This is essential for analyzing phases where acceleration is involved.

Constant Velocity Motion

This involves motion in which an object moves at a steady speed without acceleration. The displacement in this scenario is calculated simply as the product of speed and time, which is vital when analyzing segments of motion where acceleration is absent.

Transcript

00:01 Okay.

00:03 So for this problem, we have a chameleon who is extending its tongue to catch an insect.

00:10 And initially, for the first 20 milliseconds, the tongue as it's reaching out is extending with an acceleration of 250 meters per second square.

00:21 And then for the following 30 meters per second, we know that the velocity is constant.

00:26 So we're going to use this information here to calculate the total.

00:32 Distance that the tongue has been extended.

00:35 And just as a reminder, we always know that when we are calculating position, velocity, and acceleration, we know that when we go in this direction, we're calculating slope to yield the subsequent value, so from position to velocity, calculate the slope of the position at a certain point in time to give us the velocity at that certain point in time.

01:00 And when we move in the other direction, just like so, we're finding the area under the curve.

01:08 Okay? so i think the first thing that will kind of help us out here is if we actually drew a diagram to see what's going on, and we can start with acceleration.

01:17 And let's draw a little graph here.

01:21 It doesn't need to be the prettiest thing, but here we're going to have time.

01:25 Let's do that in terms of milliseconds.

01:27 Okay.

01:28 And we're going to have on this end the acceleration.

01:31 Acceleration, the tongue is only going in one direction for this problem.

01:34 So let's say acceleration in the x direction.

01:36 And that's going to be in meters per second squared.

01:40 Okay, so we know that we have meters per second squared here, but we're using milliseconds here.

01:45 So we're going to have to be careful with our units.

01:48 And as a matter of fact, let's make it easier for ourselves now and just have time also in terms of seconds.

01:56 So we're going to have to convert.

01:57 So we know that 20 milliseconds is going to be 0 .2 seconds, and 30 milliseconds is going to be 0 .30 seconds.

02:06 There.

02:07 Okay, so we know that for the first 20 milliseconds, so from zero to 0 .2 seconds, the acceleration's constant and it's constant at 250 meters per second square.

02:27 So 250.

02:28 And then we know that for the subsequent 30 milliseconds, the velocity is constant.

02:34 And so we already know that when the velocity is constant, there's no acceleration.

02:38 And there's no change in velocity and acceleration is defined as the change in velocity.

02:45 So we know that the acceleration is going to drop down to zero for the remaining remaining 30 milliseconds.

02:55 So that's going to bring us 30 plus 20 is 50.

02:58 So we're going to have a total of 0 .5 seconds there.

03:03 Okay.

03:04 And so we're trying to get all the way to x, the displacement of the tongue.

03:07 And right now we have a curve of acceleration.

03:11 And so let's start by going to velocity.

03:15 So what is the speed of the tongue? and then once we know the speed of the tongue, we can calculate the displacement or the total length of the tongue.

03:24 And so we can split this graph into two regions.

03:30 This is region one right here, this from here to here.

03:35 And region two is going to be here to here.

03:38 This is one...

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