Answer:
a.![\rm -1.49\ m/s^2.](https://tex.z-dn.net/?f=%5Crm%20-1.49%5C%20m%2Fs%5E2.)
b. ![\rm 50.49\ m.](https://tex.z-dn.net/?f=%5Crm%2050.49%5C%20m.)
Explanation:
<u>Given:</u>
- Velocity of the particle, v(t) = 3 cos(mt) = 3 cos (0.5t) .
<h2>
(a):</h2>
The acceleration of the particle at a time is defined as the rate of change of velocity of the particle at that time.
![\rm a = \dfrac{dv}{dt}\\=\dfrac{d}{dt}(3\cos(0.5\ t ))\\=3(-0.5\sin(0.5\ t.))\\=-1.5\sin(0.5\ t).](https://tex.z-dn.net/?f=%5Crm%20a%20%3D%20%5Cdfrac%7Bdv%7D%7Bdt%7D%5C%5C%3D%5Cdfrac%7Bd%7D%7Bdt%7D%283%5Ccos%280.5%5C%20t%20%29%29%5C%5C%3D3%28-0.5%5Csin%280.5%5C%20t.%29%29%5C%5C%3D-1.5%5Csin%280.5%5C%20t%29.)
At time t = 3 seconds,
![\rm a=-1.5\sin(0.5\times 3)=-1.49\ m/s^2.](https://tex.z-dn.net/?f=%5Crm%20a%3D-1.5%5Csin%280.5%5Ctimes%203%29%3D-1.49%5C%20m%2Fs%5E2.)
<u>Note</u>:<em> The arguments of the sine is calculated in unit of radian and not in degree.</em>
<h2>
(b):</h2>
The velocity of the particle at some is defined as the rate of change of the position of the particle.
![\rm v = \dfrac{dr}{dt}.\\\therefore dr = vdt\Rightarrow \int dr=\int v\ dt.](https://tex.z-dn.net/?f=%5Crm%20v%20%3D%20%5Cdfrac%7Bdr%7D%7Bdt%7D.%5C%5C%5Ctherefore%20dr%20%3D%20vdt%5CRightarrow%20%5Cint%20dr%3D%5Cint%20v%5C%20dt.)
For the time interval of 2 seconds,
![\rm \int\limits^2_0 dr=\int\limits^2_0 v\ dt\\r(t=2)-r(t=0)=\int\limits^2_0 3\cos(0.5\ t)\ dt](https://tex.z-dn.net/?f=%5Crm%20%5Cint%5Climits%5E2_0%20dr%3D%5Cint%5Climits%5E2_0%20v%5C%20dt%5C%5Cr%28t%3D2%29-r%28t%3D0%29%3D%5Cint%5Climits%5E2_0%203%5Ccos%280.5%5C%20t%29%5C%20dt)
The term of the left is the displacement of the particle in time interval of 2 seconds, therefore,
![\Delta r=3\ \left (\dfrac{\sin(0.5\ t)}{0.05} \right )\limits^2_0\\=3\ \left (\dfrac{\sin(0.5\times 2)-sin(0.5\times 0)}{0.05} \right )\\=3\ \left (\dfrac{\sin(1.0)}{0.05} \right )\\=50.49\ m.](https://tex.z-dn.net/?f=%5CDelta%20r%3D3%5C%20%5Cleft%20%28%5Cdfrac%7B%5Csin%280.5%5C%20t%29%7D%7B0.05%7D%20%5Cright%20%29%5Climits%5E2_0%5C%5C%3D3%5C%20%5Cleft%20%28%5Cdfrac%7B%5Csin%280.5%5Ctimes%202%29-sin%280.5%5Ctimes%200%29%7D%7B0.05%7D%20%5Cright%20%29%5C%5C%3D3%5C%20%5Cleft%20%28%5Cdfrac%7B%5Csin%281.0%29%7D%7B0.05%7D%20%5Cright%20%29%5C%5C%3D50.49%5C%20m.)
It is the displacement of the particle in 2 seconds.
Answer:
≈933.3kg/m^3
Explanation:
Density=Mass/Volume
11200kg/12.0= 933.3333kg/m^3
Answer:
In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form, If the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2.0 m/s.
Speed = Wavelength x Wave Frequency. In this equation, wavelength is measured in meters and frequency is measured in hertz (Hz), or number of waves per second. Therefore, wave speed is given in meters per second, which is the SI unit for speed.
Explanation:
can i get the crown please
It should be the B
Low frequency and long wavelength
Answer:
The mass of the mud is 3040000 kg.
Explanation:
Given that,
length = 2.5 km
Width = 0.80 km
Height = 2.0 m
Length of valley = 0.40 km
Width of valley = 0.40 km
Density = 1900 Kg/m³
Area = 4.0 m²
We need to calculate the mass of the mud
Using formula of density
![\rho=\dfrac{m}{V}](https://tex.z-dn.net/?f=%5Crho%3D%5Cdfrac%7Bm%7D%7BV%7D)
![m=\rho\times V](https://tex.z-dn.net/?f=m%3D%5Crho%5Ctimes%20V)
Where, V = volume of mud
= density of mud
Put the value into the formula
![m=1900\times4.0\times0.40\times10^{3}](https://tex.z-dn.net/?f=m%3D1900%5Ctimes4.0%5Ctimes0.40%5Ctimes10%5E%7B3%7D)
![m =3040000\ kg](https://tex.z-dn.net/?f=m%20%3D3040000%5C%20kg)
Hence, The mass of the mud is 3040000 kg.