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sladkih [1.3K]
1 year ago
12

The position of an object is given by x = at3 - bt2 + ct,where a = 4.1 m/s3, b = 2.2 m/s2, c = 1.7 m/s, and x and t are in SI un

its. What is the instantaneous acceleration of the object when t = 4.1 s?
Physics
1 answer:
Elza [17]1 year ago
6 0

Answer:

The answer to your question is: 15 m/s2

Explanation:

Equation    x = at3 - bt2 + ct

a = 4.1 m/s3

b = 2.2 m/s2

c = 1.7 m/s

First we find  x at t = 4.1 s

x = 4.1(4.1)3 - 2.2(4.1)2 + 1.7(4.1)

x = 4.1(68.921) - 2.2(16.81) + 6.97

x = 282.58 - 36.98 + 6.98

x = 252.58 m

Now we find speed

v = x/t = 252.58/ 4.1 = 61.6 m/s

Finally

acceleration = v/t = 61.6/4.1 = 15 m/s2

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Calculate the mass of the air contained in a room that measures 2.50 m x 5.50 m x 3.00 m if the density of air is 1.29 g/dm3.53.
Law Incorporation [45]

Answer:

5.32\cdot 10^4 g

Explanation:

First of all, we need to find the volume of the room, which is given by

V=2.50 m \cdot 5.50 m \cdot 3.00 m =41.3 m^3

Now we  can find the mass of the air by using

m=dV

where

d=1.29 g/dm^3 is the density of the air

V=41.3 m^3 = 41,300 dm^3 is the volume of the room

Substituting,

m=(1.29)(41300)=5.32\cdot 10^4 g

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2 years ago
A violin with string length 32 cm and string density 1.5 g/cm resonates in its fundamental with the first overtone of a 2.0-m or
love history [14]

Answer:

T=1022.42 N

Explanation:

Given that

l = 32 cm ,μ = 1.5 g/cm

L =2 m  ,V= 344 m/s

The pipe is closed so n= 3 ,for first over tone

f=\dfrac{nV}{4L}

f=\dfrac{3\times 344}{4\times 2}

f= 129 Hz

The tension in the string given as

T = f²(4l²) μ

Now by putting the values

T = f²(4l²) μ

T = 129² x (4 x 0.32²)  x 1.5 x  10⁻³ x 100

T=1022.42 N

6 0
2 years ago
A typical mattress has a network of springs that provide support. If you sit on a mattress, the springs compress. A heavier pers
GenaCL600 [577]

Answer:

Explanation:

Spring has a tendency to store energy in them and deform its shape when force is applied on it. Once the applied force is removed it regains its original shape and size.

It is in helical shape and is used in mattress to give structure and support. Spring have elastic nature and follows spring forces, F = k * x

where is the applied force, k is the spring constant and x is the amount of extension.

When a heavier person sits on a mattress, more weight is applied on springs and they form coils, as weight is removed they regains its shape again.

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1 year ago
A car has a mass of 1.00 × 103 kilograms, and it has an acceleration of 4.5 meters/second2. What is the net force on the car
Novay_Z [31]

Answer:

4.5 *10^{3}\ kgm/s^{2}

Explanation:

Given:

Mass= 1.00 * 10^{3} \ kilograms,\\Acceleration =4.5\  meters/second^{2}

As we know that

Force=Mass * Acceleration

Putting the value of mass and Acceleration  we get ,

Force\  = \ 1.00 * 10^{3} * 4.5\ m/s^{2}

Force\  =4.5 * \ 10^{3} \  kgm/s^{2}

Therefore Net force is :4.5 *10^{3}\ kgm/s^{2}

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1 year ago
Two mating steel spur gears are 20 mm wide, and the tooth profiles have radii of curvature at the line of contact of 10 and 15 m
Rom4ik [11]

Answer:

a) The maximum contact pressure is 274.58 MPa and the width of contact is 0.058 mm

b) The maximum shear stress is 82.37 MPa at a distance of 0.023 mm

Explanation:

Given data:

L = 20 mm

F = 250 N

r₁ = 10 mm

r₂ = 15 mm

v = 0.3

E = 2.07x10⁵ MPa

A=\frac{1-V_{1}^{2}  }{E_{1} }-\frac{1-V_{2}^{2}  }{E_{2} } =\frac{1-0.3^{2} }{2.07x10^{5} } *2=8.79x10^{-6}

a) The maximum contact pressure is:

P=0.564*\sqrt{\frac{F*(\frac{1}{r_{1} }+\frac{1}{r_{2} })  }{LA} } =0.564*\sqrt{\frac{250*(\frac{1}{10} +\frac{1}{15} )}{20*8.79x10^{-6} } } =274.58MPa

The width of contact is:

b=1.13*\sqrt{\frac{FA}{L(\frac{1}{r_{1} }+\frac{1}{r_{2} })  } } =1.13*\sqrt{\frac{250*8.79x10^{-6} }{20*(\frac{1}{10} +\frac{1}{15} )} } =0.029mm\\2*b=0.058mm

b) According the graph elastic stresses below the surface, for v = 0.3, the maximum shear stress is

T = 0.3*P = 0.3 * 274.58 = 82.37 MPa

At a distance of

0.8*b = 0.8*0.029 = 0.023 mm

6 0
2 years ago
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