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3 years ago

A particle moves along the x-axis so that its velocity at anytime is t greater than or equal to 0 is given by v(t)=1-sin(2pi t)

1 answer:

5 0

A) We differentiate the expression for velocity to obtain an expression for acceleration:
v(t) = 1 - sin(2πt)
dv/dt = -2πcos(2πt)
a = -2πcos(2πt)

b) Any value of t can be plugged in as long as it is greater than or equal to 0.

c) we integrate the expression of velocity to find an expression for displacement:
∫v(t) dt = ∫ 1 - sin(2πt) dt
x(t) = t + cos(2πt)/2π + c
x(0) = 0
0 = = + cos(0)/2π + c
c = -1/2π
x(t) = t + cos(2πt)/2π -1/2π

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If a blender is plugged into a 168 V outlet that supplies 80.8 A of current, what amount of

VladimirAG [237]

Answer:

Power = 13.5744 kilowatts

Explanation:

Power is the rate at which work is done. ... Great power means a large amount of work or energy developed in a short time. For example, when a powerful car accelerates rapidly, it does a large amount of work and consumes a large amount of fuel in a short time.

Formula for power = work/time

= IVT/T

= IV

Where I is the current

And V is the voltage

The voltage V supply = 168 v

The current A supply = 80.8 A

Power = 80.8*168

Power = 13574.4 watts

Power = 13.5744 kilowatts

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3 years ago

Explain why the speed of light is lower than<br> 3.0 x 108 m/s as it goes through different media.

jekas [21]

Answer:

Sample Response: In a vacuum, there are no atoms or particles that interfere with the path of light. However, in other media, the speed of light is lower than 3.0 × 108 m/s because the wave is continuously absorbed and re-emitted by each atom in its path. The differences in speed are due to the composition of the medium and the density of the particles in the medium.

Explanation:

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3 years ago

A traffic accident detective measures the skid marks left by a car, 825kg. He determines that the distance between the point tha

deff fn [24]

Doing a force balance on the car:
ma = Fr
ma = μmg
a = μg
a = 0.3(9.81)
a = 29.43 m/s2

Using the formula:
2ax = v2
2(29.43)(34) = v2
v = 44.74 m/s = 161.05 km/h

The car was going 44.74 m/s or 161.05 kph when the brakes were applied.

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3 years ago

Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point

RideAnS [48]

Answer:

a) 2.33 m/s

b) 5.21 m/s

c) 882 m³

Explanation:

Using the concept of continuity equation

for flow through pipes

$A_{1}\times V_{1} = A_{2}\times V_{2}$

Where,

A = Area of cross-section

V = Velocity of fluid at the particular cross-section

given:

$A_{1} = 0.070 m^{2}$

$V_{1} = 3.50 m/s$

a) $A_{2} = 0.105 m^{2}$

substituting the values in the continuity equation, we get

$0.070\times 3.50 = 0.105\times V_{2}$

$V_{2} = \frac{0.070\times 3.5}{0.150}m/s$

$V_{2} = 2.33m/s$

b) $A_{2} = 0.047 m^{2}$

substituting the values in the continuity equation, we get

$0.070\times 3.50 = 0.047\times V_{2}$

$V_{2} = \frac{0.070\times 3.5}{0.047}m/s$

$V_{2} = 5.21m/s$

c) we have,

Discharge $Q = Area (A)\times Velocity(V)$

thus from the given value, we get

$Q = 0.070m^{2}\times 3.5m/s\$

$Q = 0.245 m^{3}/s$

Also,

Discharge $Q = \frac{volume}{time}$

given time = 1 hour = 1 ×3600 seconds

substituting the value of discharge and time in the above equation, we get

$0.245m^{3}/s = \frac{volume}{3600s}$

$0.245m^{3}/s\times 3600 = Volume$

volume of flow = $882 m^{3}$

8 0

3 years ago

A bullet with a mass of 0.1 kg is travelling at

mel-nik [20]

The block with the bullet lodged in the block is now travelling at 2.133 m/s.

<h3>What is momentum conservation principle?</h3>

When there is no external force acting on the system, the momentum remains conserved.

For inelastic collision, after collision both objects travel with common speed.

m1u1 + m2u2 =(m1 +m2)v

Substitute initial velocity of bullet u1 =320 m/s , initial velocity of block u2 =0, mass of bullet m1 = 0.1 kg and mass of block m2 = 14.9 kg.

Solve for the final velocity of bullet,

0.1 x 320 + 14.9 x 0 = (0.1 +14.9) x v

v = 2.133 m/s

Thus, the block with the bullet lodged in block now travelling at 2.133 m/s.

Learn more about momentum conservation principle.

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2 years ago