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4 years ago

Ive tried numerous methods, but I cant seem to get this right. Please help, and explain step by step.

1 answer:

3 0

Well, just for fun, let's see hat the form of the limit is
v = dx/dt = b + 3 c t^2 
= 1.5 + 1.92 t^2 
========================= 
now 
from 1 to 3 
x(3)= 1.5*3 +.64*27=4.5+17.28 
= 21.78 
x(1) = 1.5+.64 = 2.14 
so 
x(3)-x(1) = 19.64 
delta t = 3 - 1 = 2 seconds 
so 
v during interval = 19.64/2 
= 9.82 m/s 
now check that with calculus v in the middle of that range 
v(2) =1.5+ 1.92 (4) = 9.18 m/s 
that makes sense, the parabola is headed up so the instant speed i the middle should be a bit less than average.

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On an essentially frictionless, horizontal ice rink, a skater moving at 5.0 m/s encounters a rough patch that reduces her speed

madreJ [45]

Answer:

The length of the rough patch is 4.345 meters.

Explanation:

According to the Work-Energy Theorem, change in kinetic energy is equal to the dissipated work due to friction. That is:

$K_{1} = K_{2} + W_{loss}$

Where:

$K_{1}$ , $K_{2}$ - Initial and final kinetic energy, measured in joules.

$W_{loss}$ - Work losses due to friction.

By applying definitions of kinetic energy and work, the expression described above is expanded:

$\frac{1}{2}\cdot m \cdot v_{1}^{2} = \frac{1}{2}\cdot m \cdot v_{2}^{2} + f \cdot \Delta s$

Where:

$v_{1}$ , $v_{2}$ - Initial and final speed of the skater, measured in meters per second.

$m$ - Mass of the skater, measured in kilograms.

$\Delta s$ - Length of the rough patch, measured in meters.

$f$ - Friction force, measured in newtons.

According to the statement, friction force is represented by the following expression:

$f = r \cdot m \cdot g$

Where:

$r$ - Ratio of friction force to weight, dimensionless.

$g$ - Gravitational constant, measured in meters per square second.

Then,

$\frac{1}{2}\cdot m \cdot v_{1}^{2} = \frac{1}{2}\cdot m \cdot v_{2}^{2} + r \cdot m \cdot g \cdot \Delta s$

The equation is simplified algebraically and patch length is cleared afterwards:

$\frac{1}{2}\cdot (v_{1}^{2}-v_{2}^{2}) = r \cdot g \cdot \Delta s$

$\Delta s = \frac{v_{1}^{2}-v_{2}^{2}}{2 \cdot r \cdot g }$

Given that $v_{1} = 5\,\frac{m}{s}$ , $v_{2} = 2.5\,\frac{m}{s}$ , $r = 0.22$ and $g = 9.807 \,\frac{m}{s^{2}}$ , the length of the rough patch is:

$\Delta s = \frac{\left(5\,\frac{m}{s} \right)^{2}-\left(2.5\,\frac{m}{s} \right)^{2}}{2\cdot (0.22)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}$

$\Delta s = 4.345\,m$

The length of the rough patch is 4.345 meters.

6 0

3 years ago

Atoms of what two elements are in every organic compound?

Georgia [21]

Carbon atoms and hydrogen I hope this helps

8 0

3 years ago

object carries a charge of -8.1 ÂµC, while another carries a charge of -2.0 ÂµC. How many electrons must be transferred from the

LenKa [72]

Number of electrons transferred: $1.91\cdot 10^{13}$

Explanation:

The charge on the first object is

$Q_1 = -8.1\mu C$

while the charge on the 2nd object is

$Q_2=-2.0 \mu C$

When they are in contact, the final charge on each object will be

$Q=\frac{Q_1+Q_2}{2}=\frac{-8.1+(-2.0)}{2}=-5.05 \mu C$

So, the amount of charge (electrons) transferred from the 1st object to the 2nd object is

$\Delta Q = Q_1 - Q = -8.1 -(5.05)=-3.05 \mu C = -3.05\cdot 10^{-6}C$

The charge of one electron is

$e=-1.6\cdot 10^{-19}C$

Therefore, the number of electrons transferred is

$N=\frac{Q}{e}=\frac{-3.05\cdot 10^{-6}}{-1.6\cdot 10^{-19}}=1.91\cdot 10^{13}$

Learn more about electrons:

brainly.com/question/2757829

#LearnwithBrainly

8 0

3 years ago

Imagine you had a bar of gold and decided to cut in half. You repeated this process until eventually you could no longer cut the

nydimaria [60]

This would prove that gold is an element. No matter how far down you
examine it, you never find any particles of anything except gold.

An example of a different case is salt.
-- Imagine you had a block of salt and decided to cut it in half.
-- If you repeated this process, then eventually, at some point, you'd have
a tiny particle of salt in front of you, just like before. BUT ...
-- Just as you were getting ready to cut this one in half, you'd notice that this
particle of salt is different. It's one atom of sodium stuck to one atom of chlorine,
and if you cut it in half, you would not have ANY salt. 

This would prove that salt is a compound, made of atoms of two or more elements.

3 0

4 years ago

Read 2 more answers

A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 29.6 m/s. At the same time, it h

inessss [21]

If the vertical component is 29.6 m/s down, and the horizontal component
is 54.8 m/s parallel to the surface, then the magnitude of the slanty vector is

√(29.6² + 54.8²) = √(876.16 + 3003.04) = √3879.2 = 62.28 m/s .

That's 139 mph ! Wow !

6 0

3 years ago