<< 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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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