Answer:
v₀ = 9,798 ft / s
Explanation:
We can solve this problem with kinematics in one dimension, when the train stops the speed is zero, the acceleration is negative so that the train stops. Let's use the equation
v² = v₀² - 2 a d
v = 0
v₀ = √2 a d
In the problem it indicates that the acceleration is g / 2, we substitute
v₀ = √2 (g / 2) d
Let's calculate
v₀ = √ 2 32/2 3 = √32 3
v₀ = 9,798 ft / s
Answer
A sonic boom is a continuous effect that occurs while the object is travelling at supersonic speeds.
Answer
given,
time = 10 s
ship's speed = 5 Km/h
F = m a
a is the acceleration and m is mass.
In the first case
F₁=m x a₁
where a₁ = difference in velocity / time
F₁ is constant acceleration is also a constant.
Δv₁ = 5 x 0.278
Δv₁ = 1.39 m/s

a₁ = 0.139 m/s²
F₂ =m x a₂
F₃ = F₂ + F₁
Δv₃ = 19 x 0.278
Δv₃ = 5.282 m/s
a₃=Δv₂ / t

a₃ = 0.5282 m²/s
m a₃=m a₁ + m a₂
a₃ = a₂ + a₁
0.5282 = a₂ + 0.139
a₂=0.3892 m²/s
F₂ = m x 0.3892...........(1)
F₁ = m x 0.139...............(2)
F₂/F₁
ratio = 
ratio = 2.8
Answer:
Explained
Explanation:
A) The total energy of the system is defined by the energy at maximum amplitude, which we'll call A. At that point, the energy of the system is
E = 1/2×m×A^2;
since energy is conserved, this is also the total amount of energy that the system ever has.
So at x=1/2A,
the potential energy of the system is 1/8×m×A^2
which is one-fourth of the system's total energy. Therefore, the remaining three-fourths is kinetic.
B) (i) Doubling the maximum amplitude will quadruple the total energy:

(ii) Doubling the maximum amplitude will double the maximum velocity

(iii) Doubling the maximum amplitude will double the maximum acceleration: m×a = -k(2A)
(iv) Doubling the maximum amplitude leaves the period unchanged:
(neither m nor k has changed).