What else can we learn by examining the equation
We see that:
displacement depends on the square of the elapsed time when acceleration is not zero. In
[link] , the dragster covers only one fourth of the total distance in the first half of the elapsed time
if acceleration is zero, then the initial velocity equals average velocity (
) and
becomes
Solving for final velocity when velocity is not constant (
)
A fourth useful equation can be obtained from another algebraic manipulation of previous equations.
If we solve
for
, we get
Substituting this and
into
, we get
Calculating final velocity: dragsters
Calculate the final velocity of the dragster in
[link] without using information about time.
Strategy
Draw a sketch.
The equation
is ideally suited to this task because it relates velocities, acceleration, and displacement, and no time information is required.
Solution
1. Identify the known values. We know that
, since the dragster starts from rest. Then we note that
(this was the answer in
[link] ). Finally, the average acceleration was given to be
.
2. Plug the knowns into the equation
and solve for
Thus
To get
, we take the square root:
Discussion
145 m/s is about 522 km/h or about 324 mi/h, but even this breakneck speed is short of the record for the quarter mile. Also, note that a square root has two values; we took the positive value to indicate a velocity in the same direction as the acceleration.
An examination of the equation
can produce further insights into the general relationships among physical quantities:
The final velocity depends on how large the acceleration is and the distance over which it acts
For a fixed deceleration, a car that is going twice as fast doesn't simply stop in twice the distance—it takes much further to stop. (This is why we have reduced speed zones near schools.)
Putting equations together
In the following examples, we further explore one-dimensional motion, but in situations requiring slightly more algebraic manipulation. The examples also give insight into problem-solving techniques. The box below provides easy reference to the equations needed.
Summary of kinematic equations (constant
)
Calculating displacement: how far does a car go when coming to a halt?
On dry concrete, a car can decelerate at a rate of
, whereas on wet concrete it can decelerate at only
. Find the distances necessary to stop a car moving at 30.0 m/s
(about 110 km/h) (a) on dry concrete and (b) on wet concrete. (c) Repeat both calculations, finding the displacement from the point where the driver sees a traffic light turn red, taking into account his reaction time of 0.500 s to get his foot on the brake.
Strategy
Draw a sketch.
In order to determine which equations are best to use, we need to list all of the known values and identify exactly what we need to solve for. We shall do this explicitly in the next several examples, using tables to set them off.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
Got questions? Join the online conversation and get instant answers!