<< 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

Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli’s principle to explain these phenomena.
Aliraza Reply
Plz answer the question ☝️☝️
Aliraza
what's the basic si unit of acceleration
ELLOIN Reply
Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.
Fabian Reply
Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.
Muhammad Reply
Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.
Muhammad
Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0m by 8.5m whose uniform depth is 1 .8m.
Henny Reply
how solve this problem?
Foday
P(pressure)=density ×depth×acceleration due to gravity Force =P×Area(28.0x8.5)
Fomukom
for the answer to complete, the units need specified why
muqaddas Reply
That's just how the AP grades. Otherwise, you could be talking about m/s when the answer requires m/s^2. They need to know what you are referring to.
Kyle
Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
Alexia Reply
how would I work this problem
Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
what is angular velocity
Obaapa Reply
angular velocity can be defined as the rate of change in radian over seconds.
Fidelis
Why does earth exert only a tiny downward pull?
Mya Reply
hello
Islam
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
Kintu
physics can be defined as the natural science that deals with the study of motion through space,time along with its related concepts which are energy and force
Fidelis
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
Obrian 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