Answer:
250+50=300ms-¹
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The runner's acceleration during this time interval is 10
<u>Given the following data:</u>
- Initial velocity, U = 0 m/s (since the sprinter is starting from rest).
- Final velocity, V = 10.0 m/s
To calculate the runner's acceleration during this time interval, we would use the first equation of motion;
Mathematically, the first equation of motion is calculated by using the formula;
<u>Where:</u>
- U is the initial velocity.
- t is the time measured in seconds.
Substituting the given parameters into the formula, we have;
Therefore, the runner's acceleration during this time interval is 10
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Answer:
Option C : 290 J
Explanation:
We can use conservation of energy to estimate the kinetic energy when the object hits the ground:
When the object is at its initial height of 15 meters, it velocity is zero (falls from this position), therefore the total energy it possesses is due to potential energy given by the expression:
Joules
At the moment the object hits the ground from its free fall, its potential energy is zero, while its kinetic energy must equal the rest. So at that moment the object's kinetic energy must be 294 Joules.
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
Answer:
g = 0.85 m
Explanation:
g =
were; g is the acceleration due to Earth's gravity, G is Newton's gravitation constant (6.674 x N), M is the mass of the earth (5.972 x kg), and h is the distance of meteoroid to the earth.
h = 3.40 x R
= 3.40 x 6371 km
h = 21661.4 km
= 21661400 m
Thus,
g =
=
= 0.84944
g = 0.85 m
The acceleration due to the Earth's gravitation is 0.85 m.