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The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion $ s = 2 \sin \pi t + 3 \cos \pi t $, where $ t $ is measured in seconds.

(a) Find the average velocity during each time period: (i) $ [1, 2] $ (ii) $ [1, 1.1] $ (iii) $ [1, 1.01] $ (iv) $ [1, 1.001] $(b) Estimate the instantaneous velocity of the particle when $ t =1 $.

A.$6,-4.7120,-6.13411,-6.26837$B.$-2 \pi \frac{\mathrm{cm}}{\mathrm{s}}$

04:53

Daniel J.

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 1

The Tangent and Velocity Problems

Limits

Derivatives

Brad S.

September 23, 2020

What do you understand by instantaneous velocity?

Erica G.

Hello there Brad as far as I know the physical velocity of a body in a point, or instantaneous velocity, is the velocity the body has at a specific time in a particular point of its trajectory. Instantaneous velocity, or simply velocity, is defined as the

Eric V.

What is average velocity?

Julia M.

I know this one! The average velocity of an object is its total displacement divided by the total time taken. In other words, it is the rate at which an object changes its position from one place to another. Average velocity is a vector quantity. The SI u

Doug F.

What is the term motion in physics?

Sarah H.

How are you Doug? The answer for that is in physics, motion is the phenomenon in which an object changes its position over time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and time.

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for this problem right here we have the displacement of a particle moving back and forth. Longstreet line. Um So we want to find the average velocity during each time period. We're gonna let this be a function of T. And that's to sign high tea Plus three. Co sign Haiti. So if our function in place We want to find the average velocity from 1-2 seconds. So that's going to be f of two -F of one all over. Uh 2 -1, Then that's 96. So now let's do 1.1 And 1.1. So it can be a negative 4.7. So let's get even closer. We'll do 1.01 1.01. Get about a negative six. And then we're going to go even closer at 1.001 And 1.001. So we end up getting negative 6.27. So a little bit more than negative six is about our final answer.

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