Answer:
v = 6t² + t + 2, s = 2t³ + ½ t² + 2t
59 m/s, 64.5 m
Explanation:
a = 12t + 1
v = ∫ a dt
v = 6t² + t + C
At t = 0, v = 2.
2 = 6(0)² + (0) + C
2 = C
Therefore, v = 6t² + t + 2.
s = ∫ v dt
s = 2t³ + ½ t² + 2t + C
At t = 0, s = 0.
0 = 2(0)³ + ½ (0)² + 2(0) + C
0 = C
Therefore, s = 2t³ + ½ t² + 2t.
At t = 3:
v = 6(3)² + (3) + 2 = 59
s = 2(3)³ + ½ (3)² + 2(3) = 64.5
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Answer:
fb = 240.35 Hz
Explanation:
In order to calculate the beat frequency generated by the first modes of each, organ and tube, you use the following formulas for the fundamental frequencies.
Open tube:
(1)
vs: speed of sound = 343m/s
L: length of the open tube = 0.47328m
You replace in the equation (1):
Closed tube:

L': length of the closed tube = 0.702821m

Next, you use the following formula for the beat frequency:

The beat frequency generated by the first overtone pf the closed pipe and the fundamental of the open pipe is 240.35Hz
1) First of all, let's find the resistance of the wire by using Ohm's law:

where V is the potential difference applied on the wire, I the current and R the resistance. For the resistor in the problem we have:

2) Now that we have the value of the resistance, we can find the resistivity of the wire

by using the following relationship:

Where A is the cross-sectional area of the wire and L its length.
We already have its length

, while we need to calculate the area A starting from the radius:

And now we can find the resistivity:
The work done is the same as the amount of energy increase. The formula for kinetic energy is 122
1
2
m
v
2
.
The initial KE of the car is 12(1000)×202=200,000
1
2
(
1000
)
×
20
2
=
200
,
000
joules.
The final KE of the car is 12(1000)×302=450,000
1
2
(
1000
)
×
30
2
=
450
,
000
joules.
The difference between these is the amount of work done: 450,000−200,000=250,000
450
,
000
−
200
,
000
=
250
,
000
joules.
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