Answer:
1.3m/s
Explanation:
Data given,
Mass,m=1.0kg,
Amplitude,A=0.10m,
Frequency,f=2.0Hz.
From the equation of a simple harmonic motion, the displacement of the object at a given time is define as

we can express the velocity by the derivative of the displacement,
Hence

at equilibrium, the velocity becomes

Hence if we substitute values we arrive at

v₀ = initial speed of the object = 8 meter/second
v = final speed of the object = 16 meter/second
t = time taken to increase the speed = 10 seconds
d = distance traveled by the object in the given time duration = ?
using the kinematics equation
d = (v + v₀) t/2
inserting the above values in the above equation
d = (16 + 8) (10)/2
d = 120 meter
Answer:
f = 3.09 Hz
Explanation:
This is a simple harmonic motion exercise where the angular velocity is
w² =
to find the constant (k) of the spring, we use Hooke's law with the initial data
F = - kx
where the force is the weight of the body that is hanging
F = W = m g
we substitute
m g = - k x
k =
we calculate
k =
k = 3.769 10² m
we substitute in the first equation
w² =
w = 19.415 rad / s
angular velocity and frequency are related
w = 2πf
f =
f = 19.415 / 2pi
f = 3.09 Hz
Answer:
The final velocity of the car is 26.65 m/s.
Explanation:
Given;
acceleration of the racecar, a = 6.5 m/s²
initial velocity of the car, u = 0
time of motion, t = 4.1 s
The final velocity of the car is given by;
v = u + at
where;
v is the final velocity of the car
suvstitute the givens
v = 0 + (6.5)(4.1)
v = 26.65 m/s.
Therefore, the final velocity of the car is 26.65 m/s.
Energy Density = 1/2 × ε(0) × (V/d)^2
V = 100, d = 0.01, ε(0) = 8.85 x 10^-12