2.5 Motion equations for constant acceleration in one dimension  (Page 7/8)

 Page 7 / 8

A manned rocket accelerates at a rate of ${\text{20 m/s}}^{2}$ during launch. How long does it take the rocket to reach a velocity of 400 m/s?

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

$v\phantom{\rule{0.15em}{0ex}}=\phantom{\rule{0.15em}{0ex}}{v}_{0}+\text{at}$

Rearrange to solve for $t$ .

$t=\frac{v-v{}_{0}\text{}}{a}=\frac{\text{400 m/s}-\text{0 m/s}}{{\text{20 m/s}}^{2}}=\text{20 s}$

Section summary

• To simplify calculations we take acceleration to be constant, so that $\stackrel{-}{a}=a$ 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,
$\left(\begin{array}{lll}\Delta t& =& t\\ \Delta x& =& x-{x}_{0}\\ \Delta v& =& v-{v}_{0}\end{array}}$
• The following kinematic equations for motion with constant $a$ are useful:
$x={x}_{0}+\stackrel{-}{v}t$
$\stackrel{-}{v}=\frac{{v}_{0}+v}{2}$
$v={v}_{0}+\text{at}$
$x={x}_{0}+{v}_{0}t+\frac{1}{2}{\text{at}}^{2}$
${v}^{2}={v}_{0}^{2}+2a\left(x-{x}_{0}\right)$
• In vertical motion, $y$ is substituted for $x$ .

Problems&Exercises

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

(a) $\text{10}\text{.}8\phantom{\rule{0.25em}{0ex}}\text{m/s}$

(b)

A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is $2\text{.}\text{10}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$ , and 1.85 ms $\left(\text{1 ms}={\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{s}\right)$ 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)

A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of $6\text{.20}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$ for $8\text{.}\text{10}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{s}$ . What is its muzzle velocity (that is, its final velocity)?

(a) A light-rail commuter train accelerates at a rate of $1\text{.}{\text{35 m/s}}^{2}$ . 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 $1\text{.}{\text{65 m/s}}^{2}$ . 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 ${\text{m/s}}^{2}$ ?

(a) $\text{16}\text{.}\text{5 s}$

(b) $\text{13}\text{.}\text{5 s}$

(c) $-2\text{.}{\text{68 m/s}}^{2}$

While entering a freeway, a car accelerates from rest at a rate of $2\text{.}{\text{40 m/s}}^{2}$ 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.

At the end of a race, a runner decelerates from a velocity of 9.00 m/s at a rate of $2\text{.}{\text{00 m/s}}^{2}$ . (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) $\text{20}\text{.}\text{0 m}$

(b) $-1\text{.}\text{00 m/s}$

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

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?

definition of mass of conversion
how many subject is in physics
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
the range of objects and phenomena studied in physics is
what is Linear motion
straight line motion is called linear motion
then what
Amera
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions.
Praise
what is a classical electrodynamics?
Marga
what is dynamics
Marga
dynamic is the force that stimulates change or progress within the system or process
Oze
what is the formula to calculate wavelength of the incident light
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
State the forms of energy
machanical
Ridwan
Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
correct
Akinpelu
what is mechanical wave
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
watt
Okoli
Am I correct
Okoli
it can be in kilowatt, megawatt and so
Femi
yes
Femi
correct
Jaheim
kW
Akinpelu
OK that's right
Samuel
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
What is physics
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
reasonable
Femi
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
What is a wave
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
mistakes thanks
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k