Answer:
<em>The car took 3 hours to travel 180 miles</em>
Explanation:
<u>Constant Speed Motion</u>
An object travels at constant speed if the ratio of the distance traveled by the time taken is constant.
Expressed in a simple equation, we have:
Where
v = Speed of the object
d = Distance traveled
t = Time taken to travel d.
From the equation above, we can solve for t:
The car travels at v=60 mi/h for a distance of d=180 miles. The time taken is:
t = 3 hours
The car took 3 hours to travel 180 miles
Answer:
Explanation:
When an amount of energy Q is supplied to a substance of mass m, the temperature of the substance increases by , according to the equation
where is the specific heat capacity of the substance.
In this problem, we have:
is the amount of heat supplied to the sample of gold
m = 0.1 kg = 100 g is the mass of the sample
is the specific heat capacity of gold
Solving for , we find the change in temperature
And since the final temperature was
The initial temperature was
Heres your answer to ur question
Quasi frequency = 4√6
Quasi period = π√6/12
t ≈ 0.4045
<u>Explanation:</u>
Given:
Mass, m = 20g
τ = 400 dyn.s/cm
k = 3920
u(0) = 2
u'(0) = 0
General differential equation:
mu" + τu' + ku = 0
Replacing the variables with the known value:
20u" + 400u' + 3920u = 0
Divide each side by 20
u" + 20u' + 196u = 0
Determining the characteristic equation by replacing y" with r², y' with r and y with 1 in the differential equation.
r² + 20r + 196 = 0
Determining the roots:
r = -10 ± 4√6i
The general solution for two complex roots are:
y = c₁ eᵃt cosbt + c₂ eᵃt sinbt
with a the real part of the roots and b be the imaginary part of the roots.
Since, a = -10 and b = 4√6
u(t) = c₁e⁻¹⁰^t cos 4√6t + c₂e⁻¹⁰^t sin 4√6t
u(0) = 2
u'(0) = 0
(b)
Quasi frequency:
μ =
(c)
Quasi period:
T = 2π / μ
(d)
|u(t)| < 0.05 cm
u(t) = |2e⁻¹⁰^t cos 4√6t + 5√6/6 e⁻¹⁰^t sin 4√6t < 0.05
solving for t:
τ = t ≈ 0.4045
