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Conceptual questions

When given the acceleration function, what additional information is needed to find the velocity function and position function?

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Problems

The acceleration of a particle varies with time according to the equation a ( t ) = p t 2 q t 3 . Initially, the velocity and position are zero. (a) What is the velocity as a function of time? (b) What is the position as a function of time?

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Between t = 0 and t = t 0 , a rocket moves straight upward with an acceleration given by a ( t ) = A B t 1 / 2 , where A and B are constants. (a) If x is in meters and t is in seconds, what are the units of A and B ? (b) If the rocket starts from rest, how does the velocity vary between t = 0 and t = t 0 ? (c) If its initial position is zero, what is the rocket’s position as a function of time during this same time interval?

a. A = m/s 2 B = m/s 5 / 2 ;
b. v ( t ) = a ( t ) d t + C 1 = ( A B t 1 / 2 ) d t + C 1 = A t 2 3 B t 3 / 2 + C 1 v ( 0 ) = 0 = C 1 so v ( t 0 ) = A t 0 2 3 B t 0 3/2 ;
c. x ( t ) = v ( t ) d t + C 2 = ( A t 2 3 B t 3 / 2 ) d t + C 2 = 1 2 A t 2 4 15 B t 5 / 2 + C 2 x ( 0 ) = 0 = C 2 so x ( t 0 ) = 1 2 A t 0 2 4 15 B t 0 5/2

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The velocity of a particle moving along the x- axis varies with time according to v ( t ) = A + B t −1 , where A = 2 m/s, B = 0.25 m, and 1.0 s t 8.0 s . Determine the acceleration and position of the particle at t = 2.0 s and t = 5.0 s. Assume that x ( t = 1 s ) = 0 .

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A particle at rest leaves the origin with its velocity increasing with time according to v ( t ) = 3.2 t m/s. At 5.0 s, the particle’s velocity starts decreasing according to [16.0 – 1.5( t – 5.0)] m/s. This decrease continues until t = 11.0 s, after which the particle’s velocity remains constant at 7.0 m/s. (a) What is the acceleration of the particle as a function of time? (b) What is the position of the particle at t = 2.0 s, t = 7.0 s, and t = 12.0 s?

a. a ( t ) = 3.2 m/s 2 t 5.0 s a ( t ) = 1.5 m/s 2 5.0 s t 11.0 s a ( t ) = 0 m/s 2 t > 11.0 s ;
b. x ( t ) = v ( t ) d t + C 2 = 3.2 t d t + C 2 = 1.6 t 2 + C 2 t 5.0 s x ( 0 ) = 0 C 2 = 0 therefore, x ( 2.0 s ) = 6.4 m x ( t ) = v ( t ) d t + C 2 = [ 16.0 1.5 ( t 5.0 ) ] d t + C 2 = 16 t 1.5 ( t 2 2 5.0 t ) + C 2 5.0 t 11.0 s x ( 5 s ) = 1.6 ( 5.0 ) 2 = 40 m = 16 ( 5.0 s ) 1.5 ( 5 2 2 5.0 ( 5.0 ) ) + C 2 40 = 98.75 + C 2 C 2 = −58.75 x ( 7.0 s ) = 16 ( 7.0 ) 1.5 ( 7 2 2 5.0 ( 7 ) ) 58.75 = 69 m x ( t ) = 7.0 d t + C 2 = 7 t + C 2 t 11.0 s x ( 11.0 s ) = 16 ( 11 ) 1.5 ( 11 2 2 5.0 ( 11 ) ) 58.75 = 109 = 7 ( 11.0 s ) + C 2 C 2 = 32 m x ( t ) = 7 t + 32 m x 11.0 s x ( 12.0 s ) = 7 ( 12 ) + 32 = 116 m

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Additional problems

Professional baseball player Nolan Ryan could pitch a baseball at approximately 160.0 km/h. At that average velocity, how long did it take a ball thrown by Ryan to reach home plate, which is 18.4 m from the pitcher’s mound? Compare this with the average reaction time of a human to a visual stimulus, which is 0.25 s.

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An airplane leaves Chicago and makes the 3000-km trip to Los Angeles in 5.0 h. A second plane leaves Chicago one-half hour later and arrives in Los Angeles at the same time. Compare the average velocities of the two planes. Ignore the curvature of Earth and the difference in altitude between the two cities.

Take west to be the positive direction.
1st plane: ν = 600 km/h
2nd plane ν = 667.0 km/h

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Unreasonable Results A cyclist rides 16.0 km east, then 8.0 km west, then 8.0 km east, then 32.0 km west, and finally 11.2 km east. If his average velocity is 24 km/h, how long did it take him to complete the trip? Is this a reasonable time?

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Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
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But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
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the significance of food webs for disease transmission
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food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
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Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
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cell is the smallest unit of life
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cell is the smallest unit of life
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Innocent
cell is the structural and functional unit of life
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is the fundamental units of Life
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There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
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Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
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part of a tissue or an organ being wounded or bruised.
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Binomial nomenclature
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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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