The position of the object at time t =2.0 s is <u>6.4 m.</u>
Velocity vₓ of a body is the rate at which the position x of the object changes with time.
Therefore,

Write an equation for x.

Substitute the equation for vₓ =2t² in the integral.

Here, the constant of integration is C and it is determined by applying initial conditions.
When t =0, x = 1. 1m

Substitute 2.0s for t.

The position of the particle at t =2.0 s is <u>6.4m</u>
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


Where, V = volume of mud
= density of mud
Put the value into the formula


Hence, The mass of the mud is 3040000 kg.
Answer:
Explanation:
extension in the spring = 40.4 - 31.8 = 8.6 cm = 8.6 x 10⁻² m .
kx = mg
k is spring constant , x is extension , m is mass
k x 8.6 x 10⁻² = 7.52 x 9.8
k = 856.93 N/m
= 857 x 10⁻³ KN /m
b ) Both side is pulled by force of 188 N .
Tension in spring = 188N
kx = T
856.93 x = 188
x = .219.38 m
= 21.938 cm
= 21.9 cm .
length of spring = 31.8 + 21.9
= 53.7 cm .
The resonant frequency of a circuit is the frequency
at which the equivalent impedance of a circuit is purely real (the imaginary part is null).
Mathematically this frequency is described as

Where
L = Inductance
C = Capacitance
Our values are given as


Replacing we have,



From this relationship we can also appreciate that the resonance frequency infers the maximum related transfer in the system and that therefore given an input a maximum output is obtained.
For this particular case, the smaller the capacitance and inductance values, the higher the frequency obtained is likely to be.