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Alinara [238K]
3 years ago
13

A particle moves along the x axis so that its velocity at time t is given by v(t)=

Physics
1 answer:
vodomira [7]3 years ago
6 0

Answer:

a = 0.7267 ,  acceleration is positive therefore the speed is increasing  

Explanation:

The definition of acceleration is

         a = dv / dt

they give us the function of speed

         v = - (t-1) sin (t² / 2)

         a = - sin (t²/2) -  (t-1) cos (t²/2)  2t / 2

         a = - sin (t²/2) - t (t-1)  cos (t²/2)

the acceleration for t = 4 s

          a = - sin (4²/2) - 4 (4-1) cos (4²/2)

          a = -sin 8 - 12 cos 8

remember that the angles are in radians

          a = 0.7267

the problem does not indicate the units, but to be correct they must be m/s²

We see that the acceleration is positive therefore the speed is increasing

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3 years ago
Based on Archimedes' principle, the greatest buoyant force an object can experience in water is determined by which quantity?
ValentinkaMS [17]

Answer:

B. The object's volume

Explanation:

When an object is immersed in a fluid, it experiences an upward force which is called buoyant force. The magnitude of the buoyant force is given by:

B=\rho_f V_{disp} g

where

\rho_f is the density of the fluid in which the object is immersed

V_{disp} is the volume of the fluid displaced by the object

g is the acceleration due to gravity

When the object is totally immersed in the fluid, V_{disp} corresponds to the volume of the object; when the object is only partially immersed, V_{disp} corresponds only to the volume of the part of the object immersed.

From the formula, we see that the greatest buoyant force is experienced by the object when it is fully immersed. Moreover, we see that the buoyant force depends only on one property of the object: its volume. Therefore, the correct choice is

B. The object's volume

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3 years ago
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3 years ago
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The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ????h=0.209 m and mass 4.32 kg , an
Stolb23 [73]

Answer:

r= 98.3 mm

Explanation:

For rim

R= 0.209 m

M= 4.32 kg

For rods

m= 7.37 kg

L= 2 R= 2 x 0.209 = 0.418 m

The Total moment of inertia of the  wagon

I=MR²+2 x 1/12 m L²

Now by putting the values

I=4.32\times 0.209^2+2\times \dfrac{1}{12}\times 7.73\times 0.418^2\ kg.m^2

I=0.413 kg.m²

For disk:

t= 0.0462 m

Density ρ = 5990 kg/m³

Lets take r is the radius of disk

So the mass of the disc

m'=ρ πr² t

The moment of inertia of disc

I'=1/2 m'r²

I'=1/2 x r² x ρ πr² t

Given that

I = I'

1/2 x r² x ρ πr² t = 0.413 kg.m²

1/2 x r³ x ρ π t = 0.413

r³ x ρ π t = 0.826

r^3=\dfrac{0.826}{\pi \times 5990 \times 0.0462}

r³=0.00095

r=0.0983 m

r= 98.3 mm

8 0
3 years ago
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