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 well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is
$2\text{.}\text{10}\times {\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$ , and 1.85 ms
$(\text{1 ms}={\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{s})$ 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)
A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of
$6\text{.20}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$ for
$8\text{.}\text{10}\times {\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{s}$ . 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?
Questions & Answers
find the 15th term of the geometric sequince whose first is 18 and last term of 387
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.