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Numerade Educator

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Problem 5 Medium Difficulty

If a ball is thrown into the air with a velocity of $ 40 ft/s $, its height in feet $ t $ seconds later is given by $ y = 40t - 16t^2 $.

(a) Find the average velocity for the time period beginning when $ t = 2 $ and lasting
(i) 0.5 seconds (ii) 0.1 seconds
(iii) 0.05 seconds (iv) 0.01 seconds
(b) Estimate the instantaneous velocity when $ t = 2 $.

Answer

A.
(i) $-32 \mathrm{ft} / \mathrm{s}$
(ii) $-25.6 \mathrm{ft} / \mathrm{s}$
(iii) $-24.8 \mathrm{ft} / \mathrm{s}$
(iv) $-24.16 \mathrm{ft} / \mathrm{s}$
B.$-24 \frac{f t}{s}$

Discussion

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Samantha G.

March 17, 2019

seeing someone else use excel is not helpful in teaching how to complete a problem like this. As someone who struggles with understanding math computation, I need to see the problem worked out and broken into steps.

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Angel S.

June 8, 2020

I agree with Samantha. This is not helpful at all.

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Jessica G.

September 23, 2020

What is a average velocity?

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Holly S.

September 23, 2020

Average velocity can be defined as the displacement divided by the time. Hope that helps Jessica.

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Alexis B.

September 23, 2020

Can someone explain what the Velocity is?

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Sam L.

September 23, 2020

Hey Jessica, Velocity is defined as a vector measurement of the rate and direction of motion. Hope that helps.

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Frank V.

September 23, 2020

I'm confused by the term paucity.

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Hank S.

September 23, 2020

Paucity is the presence of something only in small or insufficient quantities or amounts; scarcity. Hope that helps Frank.

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Juan D.

August 29, 2021

If a ball is thrown into the air with an initial velocity of 42 ft/s,

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Juan D.

August 29, 2021

Video Transcript

Okay. This question is having you compare average velocity and instantaneous velocity average velocity average velocity is going to be the change in why divided by the change in T. And the instantaneous velocity is what happens with the as Delta T approaches zero. Yeah. So I what I did is I put the function Y equals 40 t minus 16 T squared into the calculator from T equals to two T. Equals 2.5. I need the change in y over the change in T. So I need why at 2.5 -Y. at two Divided by 2.5 -2. Why at 2.5 I calculate a value at 2.5 and I get Why it is zero. And then I subtract why it too. Yeah, value at two And I get 16 0 -16 divided by .5. So my average velocity is I'm gonna shrink everything just a little bit. Mhm. About my plan all written down. I just wanted a little smaller so I got room to write, right, okay. Mhm. This is not working right today, let's just make it smaller. Here we go. All right, so my average about my average velocity for the first one was 0.6 0 -16 divided by .5 which is -32. This would be in feet per second from 2 to 2.1. I know why it too is 16 But what I need is why at 2.1. So you calculate value 2.1 you get 13.44 -16 divided by 0.1. So 1344 yeah minus 16 Divided by .1 is times 10. So here I get negative 25.6. Now I need the value for Yeah. 25. Okay. Mhm. Which is 14.76 minus 16 Divided by .05. Okay. Okay. That's negative. 24.8. And now I need a value at 2.01. Yeah. Okay. I get 15.75 7,58, -16 Divided by .01. Yeah. Yeah. And I'm getting negative 24.16. So they want you to estimate the instantaneous velocity at two equals 2. I would estimate It looks like it's a protein -24. Really soon we'll learn how to take the derivative of why with respect to T. And I'll take the limit of the limit of the change in why? With respect to T. As delta T approaches zero, I'm going to guess that we get about negative 24 ft/s. That's what it looks like. These are approaching. Thanks for listening and have a great day