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3 years ago

Explain integration and differentiation in simple method!

1 answer:

5 0

Differentiation in its simplest of terms means breaking something into small parts. On the other hand, integration is taking those really small parts and gluing them in the right order. In short, these terms are the direct opposite or inverses of each other. The term which can tell you how fast you are going at a moment in time at ones current location is called a derivative. The term on the other hand, which can tell you how far you have travelled if you have been keeping track of your location and your time is what an integral is referred to. It is like differentiation only needs knowledge on the local neighbourhood while integration will need the knowledge on a global knowledge.

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Calculate the work performed by an ideal Carnot engine as a cold brick warms from 150 K to the temperature of the environment, w

olga nikolaevna [1]

To solve this problem, apply the concepts related to the calculation of the work performed according to the temperature change (in an ideal Carnot cycle), for which you have to:

$W = \int\limit_{T_c}^{T_H} C (1-\frac{T_H}{T})$

Where,

C = Heat capacity of the Brick

$T_C$ = Cold Temperature

$T_H$ = Hot Temperature

Integrating,

$W = C (T_H-T_C)- T_H C ln (\frac{T_H}{T_C})$

Our values are given as

$T_H= 300K$

$T_C = 150K$

Replacing,

$W = (1) (300-150)-300(1)ln(2)$

$W = 150-300ln2$

$W = -57.94kJ \approx 58kJ$

Therefore the work perfomed by this ideal carnot engine is 58kJ

5 0

4 years ago

An object accelerates from rest to 93 m/s over a distance of 49 m. What acceleration did it experience?

Maksim231197 [3]

Answer:

$88.3ms {}^{ - 2}$

or 88.3m/s^2

Explanation:

Using suvat where we list everything that we are given

s=49m

u=0m/s

v=93m/s

a=?

t=we are not given this value, so we don't use

using a formula that doesn't involve time:

$v {}^{2} = u {}^{2} + 2as$

rearranging to find acceleration by subtracting u^2 on both sides

$v {}^{2} - u {}^{2} = 2as$

then dividing 2s on both sides

$\frac{v {}^{2} - u {}^{2} }{2s} = a$

$\frac{(93) {}^{2} - (0) {}^{2} }{2 \times(49) } = 88.3ms {}^{ - 2}$

so the acceleration is 88.3ms^-2 (1dp)

3 0

3 years ago

Which of the following is an example of qualitative data

NemiM [27]

Qualitative data is easy to explain. You either agree or disagree in writing. Wrong. You agree, disagree, or qualify. Meaning agree to somewhat extend, but not entirely. So you can agree that people should walk instead of talk in the progressive manner, but not in the impulsive manner.

3 0

4 years ago

The maximum energy a bone can absorb without breaking is surprisingly small. For a healthy human of mass 60 kg60 kg, experimenta

netineya [11]

Answer:

the maximum height a man can jump from and land rigidly upright on both feet without breaking his legs is 0.34 m

Explanation:

Mass of a healthy man = 60 kg

energy the bone can take without breaking = 200 J

If a healthy man jumps from a height 'h', he falls with an energy equal to the potential energy due to his initial height above the ground.

initial potential energy of the healthy man = mgh

where m = mass of the man

g = acceleration due to gravity = 9.81 m/s^2

h = the height above ground

==> PE = 60 x 9.81 x h = 588.6h

If we assume that all energy is absorbed in the leg bones in a rigid landing, then we can safely say that this calculated PE for a healthy man is equal to the energy his bone can absorb in the jump without breaking.

equating, we have

200 = 588.6h

the maximum height a man can jump from without breaking his legs = 200/588.6 = 0.34 m

When people jump from a height, the sudden deceleration to zero can impact a big force on the leg bones, shattering them. If the time spent in decelerating to zero is increased, the overall force on the leg bones is reduced greatly.

Bending the knees gradually on landing from a jump from a height, and then rolling increases the time spent decelerating, and reduces the impact force on the legs due to the landing. If you observe carefully you will see that this is what professional stunts men and acrobats do when they jump from a height.

5 0

3 years ago

look at the pictures. they show some people making forces. write short sentences to describe what each force is being used for

Sauron [17]

there are three picture with example and sentence

8 0

3 years ago