<< Chapter < Page Chapter >> Page >

A manned rocket accelerates at a rate of 20 m/s 2 size 12{"20 m/s" rSup { size 8{2} } } {} during launch. How long does it take the rocket reach a velocity of 400 m/s?

To answer this, choose an equation that allows you to solve for time t size 12{t} {} , given only a size 12{a} {} , v 0 size 12{v rSub { size 8{0} } } {} , and v size 12{v} {} .

v = v 0 + at size 12{v=v"" lSub { size 8{0} } + ital "at"} {}

Rearrange to solve for t size 12{t} {} .

t = v v 0 a = 400 m/s 0 m/s 20 m/s 2 = 20 s size 12{t= { {v - v"" lSub { size 8{0} } } over {a} } = { {"400 m/s" - "0 m/s"} over {"20 m/s" rSup { size 8{2} } } } ="20 s"} {}
Got questions? Get instant answers now!

Section summary

  • To simplify calculations we take acceleration to be constant, so that a - = a size 12{ { bar {a}}=a} {} at all times.
  • We also take initial time to be zero.
  • Initial position and velocity are given a subscript 0; final values have no subscript. Thus,
    Δ t = t Δ x = x x 0 Δ v = v v 0
  • The following kinematic equations for motion with constant a size 12{a} {} are useful:
    x = x 0 + v - t size 12{x=x rSub { size 8{0} } + { bar {v}}t} {}
    v - = v 0 + v 2 size 12{ { bar {v}}= { {v rSub { size 8{0} } +v} over {2} } } {}
    v = v 0 + at size 12{v=v rSub { size 8{0} } + ital "at"} {}
    x = x 0 + v 0 t + 1 2 at 2 size 12{x=x rSub { size 8{0} } +v rSub { size 8{0} } t+ { {1} over {2} } ital "at" rSup { size 8{2} } } {}
    v 2 = v 0 2 + 2 a x x 0 size 12{v rSup { size 8{2} } =v rSub { size 8{0} } rSup { size 8{2} } +2a left (x - x rSub { size 8{0} } right )} {}
  • In vertical motion, y size 12{y} {} is substituted for x size 12{x} {} .

Problems&Exercises

An Olympic-class sprinter starts a race with an acceleration of 4 . 50 m/s 2 size 12{4 "." "50 m/s" rSup { size 8{2} } } {} . (a) What is her speed 2.40 s later? (b) Sketch a graph of her position vs. time for this period.

(a) 10 . 8 m/s size 12{"10" "." 8" m/s"} {}

(b)

Line graph of position in meters versus time in seconds. The line begins at the origin and is concave up, with its slope increasing over time.
Got questions? Get instant answers now!

A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is 2 . 10 × 10 4 m/s 2 , and 1.85 ms ( 1 ms = 10 3 s ) size 12{ \( "1 ms"="10" rSup { size 8{-3} } " s" \) } {} elapses from the time the ball first touches the mitt until it stops, what was the initial velocity of the ball?

38.9 m/s (about 87 miles per hour)

Got questions? Get instant answers now!

A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of 6 .20 × 10 5 m/s 2 size 12{6 "." "20"´"10" rSup { size 8{5} } " m/s" rSup { size 8{2} } } {} for 8 . 10 × 10 4 s . What is its muzzle velocity (that is, its final velocity)?

Got questions? Get instant answers now!

(a) A light-rail commuter train accelerates at a rate of 1 . 35 m/s 2 size 12{1 "." "35 m/s" rSup { size 8{2} } } {} . How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of 1 . 65 m/s 2 size 12{1 "." "65 m/s" rSup { size 8{2} } } {} . How long does it take to come to a stop from its top speed? (c) In emergencies the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency deceleration in m/s 2 size 12{"m/s" rSup { size 8{2} } } {} ?

(a) 16 . 5 s size 12{`"16" "." "5 s"} {}

(b) 13 . 5 s size 12{"13" "." "5 s"} {}

(c) 2 . 68 m/s 2 size 12{` - 2 "." "68 m/s" rSup { size 8{2} } } {}

Got questions? Get instant answers now!

While entering a freeway, a car accelerates from rest at a rate of 2 . 40 m/s 2 size 12{2 "." "40 m/s" rSup { size 8{2} } } {} for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, check your units, and discuss whether the answer is reasonable. (d) What is the car's final velocity? Solve for this unknown in the same manner as in part (c), showing all steps explicitly.

Got questions? Get instant answers now!

At the end of a race, a runner decelerates from a velocity of 9.00 m/s at a rate of 2 . 00 m/s 2 size 12{2 "." "00 m/s" rSup { size 8{2} } } {} . (a) How far does she travel in the next 5.00 s? (b) What is her final velocity? (c) Evaluate the result. Does it make sense?

(a) 20 . 0 m size 12{"20" "." "0 m"} {}

(b) 1 . 00 m/s size 12{ - 1 "." "00"`"m/s"} {}

(c) This result does not really make sense. If the runner starts at 9.00 m/s and decelerates at 2 . 00 m/s 2 size 12{2 "." "00 m/s" rSup { size 8{2} } } {} , then she will have stopped after 4.50 s. If she continues to decelerate, she will be running backwards.

Got questions? Get instant answers now!

Professional Application:

Blood is accelerated from rest to 30.0 cm/s in a distance of 1.80 cm by the left ventricle of the heart. (a) Make a sketch of the situation. (b) List the knowns in this problem. (c) How long does the acceleration take? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking your units. (d) Is the answer reasonable when compared with the time for a heartbeat?

Got questions? Get instant answers now!

Questions & Answers

how to create a software using Android phone
Wiseman Reply
how
basra
what is the difference between C and C++.
Yan Reply
what is software
Sami Reply
software is a instructions like programs
Shambhu
what is the difference between C and C++.
Yan
yes, how?
Hayder
what is software engineering
Ahmad
software engineering is a the branch of computer science deals with the design,development, testing and maintenance of software applications.
Hayder
who is best bw software engineering and cyber security
Ahmad
Both software engineering and cybersecurity offer exciting career prospects, but your choice ultimately depends on your interests and skills. If you enjoy problem-solving, programming, and designing software syste
Hayder
what's software processes
Ntege Reply
I haven't started reading yet. by device (hardware) or for improving design Lol? Here. Requirement, Design, Implementation, Verification, Maintenance.
Vernon
I can give you a more valid answer by 5:00 By the way gm.
Vernon
it is all about designing,developing, testing, implementing and maintaining of software systems.
Ehenew
hello assalamualaikum
Sami
My name M Sami I m 2nd year student
Sami
what is the specific IDE for flutter programs?
Mwami Reply
jegudgdtgd my Name my Name is M and I have been talking about iey my papa john's university of washington post I tagged I will be in
Mwaqas Reply
yes
usman
how disign photo
atul Reply
hlo
Navya
hi
Michael
yes
Subhan
Show the necessary steps with description in resource monitoring process (CPU,memory,disk and network)
samuel Reply
What is software engineering
Tafadzwa Reply
Software engineering is a branch of computer science directed to writing programs to develop Softwares that can drive or enable the functionality of some hardwares like phone , automobile and others
kelvin
if any requirement engineer is gathering requirements from client and after getting he/she Analyze them this process is called
Alqa Reply
The following text is encoded in base 64. Ik5ldmVyIHRydXN0IGEgY29tcHV0ZXIgeW91IGNhbid0IHRocm93IG91dCBhIHdpbmRvdyIgLSBTdGV2ZSBXb3puaWFr Decode it, and paste the decoded text here
Julian Reply
what to do you mean
Vincent
hello
ALI
how are you ?
ALI
What is the command to list the contents of a directory in Unix and Unix-like operating systems
George Reply
how can i make my own software free of cost
Faizan Reply
like how
usman
hi
Hayder
The name of the author of our software engineering book is Ian Sommerville.
Doha Reply
what is software
Sampson Reply
the set of intruction given to the computer to perform a task
Noor
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask