The angular frequency of this motion is 5.46 rad/s.
The oscillation of spring is an example of Simple Harmonic Motion(SHM).
The general equation of an SHM is given by the formula.
X = Acos(wt)
Here A is the amplitude
ω is the angular frequency
T is the time
Comparing the above equation with the given condition,
X = 17.4 cm cos(5.46t)
A = 17.4 cm
ω = 5.46 rad/s
T = 1 s
Hence, the angular frequency of this motion is 5.46 rad/s.
To know more about the "general equation of SHM", refer to the link below:
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<span>The answer is 6 Joules. The kinetic energy (KE) of an object is the product of half of the mass (m) of the object and the square of its velocity (v²): KE = 1/2m*v². We know that m = 0.75 kg and that v = 4 m/s. Therefore, KE = 1/2 * 0.75 kg * (4 m/s)² = 1/2 * 0.75 kg * 16 m²/s² = 6 kg*m²/s² = 6 J.</span>
Answer:
<em>The motorboat ends up 7.41 meters to the west of the initial position
</em>
Explanation:
<u>Accelerated Motion
</u>
The accelerated motion describes a situation where an object changes its velocity over time. If the acceleration is constant, then these formulas apply:
The problem provides the conditions of the motorboat's motion. The initial velocity is 6.5 m/s west. The final velocity is 1.5 m/s west, and the acceleration is 
to the east. Since all the movement takes place in one dimension, we can ignore the vectorial notation and work with the signs of the variables, according to a defined positive direction. We'll follow the rule that all the directional magnitudes are positive to the east and negative to the west. Rewriting the formulas:
Solving the first one for t
We have
Using these values
We now compute x
The motorboat ends up 7.41 meters to the west of the initial position
While riding in a hot air balloon,
which is steadily at a speed of 1.01 m/s, and your phone accidentally falls.
<span>(a)
</span>The
speed of your phone after 4 s is:
V= u +
at
V= 1.01
+ (9.8)(4)
V=
40.21 m/s
<span>(b)
</span>The balloon
is ____ far:
V = u +
at
V= 1.01
+ (9.8)(1)
V=10.81
–distance at 1 one second
V= u +
at
V= 1.01
+ (9.8)(2)
V= 20.61-distance
at 2 seconds
V= u+ at
V=
30.41- distance at 3 seconds
V=
40.21- distance at 4 seconds
D=
102.04 m
<span>(c)
</span>If the
balloon is rising steadily at 1.01 m/s:
V= -1.1
m/s
<span> </span>
