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.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature