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VARVARA [1.3K]
3 years ago
11

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te

mperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.4. Suppose the ambient temperature TA(t) is equal to a constant 38 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object. (a) dT dt = $$ Correct: Your answer is correct. 0.4(38-T) Suppose the ambient temp TA(t) = 38cos( π 30 t) degrees Celsius (time measured in minutes). Write the DE that describes the time evolution of temperature T of the object. (b) dT dt = Correct: Your answer is correct. If we measure time in hours the differential equation in part (b) changes. What is the new differential equation? Use the letter s to denote time in hours. (c) dT ds = If we measure time in hours and we also measure temperature in degrees Fahrenheit, the differential equation in part (c) changes even more. What is the new differential equation? Use the letter F to denote temperature in degrees Fahrenheit.

Physics
1 answer:
QveST [7]3 years ago
8 0

Answer:

Please see attachment

Explanation:

Please see attachment

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A rocket, initially at rest on the ground, accelerates straight upward from rest with constant (net) acceleration 29.4 m/s2 m /
Sidana [21]

Answer:

The maximum height is 2881.2 m.

Explanation:

Given that,

Acceleration = 29.4 m/s²

Time = 7.00 s

We need to calculate the distance

Using equation of motion

s=ut+\dfrac{1}{2}at^2

Put the value into the formula

s=0+\dfrac{1}{2}\times29.4\times7^2

s=720.3\ m

We need to calculate the velocity

Using formula of velocity

v=a\times t

Put the value into the formula

v=29.4\times7

v=205.8\ m/s

We need to calculate the height

Using formula of height

H=\dfrac{v^2}{2g}

Put the value into the formula

H=\dfrac{(205.8)^2}{2\times9.8}

H=2160.9\ m

We need to calculate the maximum height

Using formula for maximum height

H'=H+s

Put the value into the formula

H'=2160.9+720.3

H'=2881.2\ m

Hence, The maximum height is 2881.2 m.

4 0
3 years ago
An object moving at 15 m/s slows uniformly at a rate of 2.0 m/s each second for 5.0 s. What is its final speed?​
NeX [460]
Hey there!

We are given ,

Acceleration, a = -2m/s^2

Initial velocity , u = 15m/s

Time , t = 5 seconds

We know that ,
V=u+at

Now , final speed ,

V = 15+(-2)(5)

V = 15-10

V = 5 m/s -> final speed

Hope this helps you dear :)
Have a good day <3

8 0
2 years ago
A neutron star and a black hole are 3.34 x 1012 m from each other at a certain point in their orbit. The neutron star has a mass
m_a_m_a [10]

Answer:

  F=1.65 x 10²⁶ N

Explanation:

Given that

Distance ,R= 3.34 x 10¹² m

Mass m₁= 2.78 x 10³⁰ kg

Mass ,m₂= 9.94 x 10³⁰ kg

we know that gravitational force F given as

F=G\dfrac{m_1m_2}{R^2}

G=Constant

G=6.67 x 10⁻¹¹ Nm²/kg²

Now by putting the values

F=6.67\times 10^{-11}\times \dfrac{2.78\times 10^{30}\times 9.94\times 10^{30}}{(3.34\times 10^{12})^2}\ N

F=1.65 x 10²⁶ N

Therefore the force between these two mass will be 1.65 x 10²⁶ N.

5 0
3 years ago
What happens to a current when the electric field in the wire increase
Gnom [1K]

Answer:

If the voltage is increased then the electric field is higher, and electron velocity (average) is proportional to this field. Then you have an increase in speed. And current is total charge passing per time unit, so current is proportional to velocity value of charge (and to voltage in resistors and wire).

Explanation:

5 0
3 years ago
If a car has a kinetic energy of 40000 J and is moving at a velocity of 25 m/s, what is the mass of the car? KE=1/2mv
ohaa [14]

Answer:

3200 Kg

Explanation:

Just apply the formula:

40.000 = 1/2 . m . 25

80.000 = 25m

m = 80.000/25

m = 3200 Kg

7 0
3 years ago
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