One light-year is the distance that light travels in vacuum
in one year. It's a unit of distance.
Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer:
1. Elastic collision
2. Inelastic collision
Explanation:
Elastic collision: collision is said to be elastic if total kinetic energy is not conserved and if there is a rebound after collision
the collision is described by the equation bellow
Inelastic collision: this type of collision occurs when the total kinetic energy of a body is conserved or when the bodies sticks together and move with a common velocity
the collision is described by the equation bellow
The speed of the sound in the xenon is 178 m/s. And the right option is b 178 m/s
<h3 /><h3>What is speed?</h3>
Speed can be defined as the ratio of the total distance traveled by a body to the total time taken.
To calculate the speed of the sound in the xenon, we use the formula below.
Formula:
- v = λf............. Equation 1
Where:
- v = Speed of the sound in xenon
- f = Frequency
- λ = Wavelength.
From the question,
Given:
- f = 440 Hz
- λ = 40.4 cm = 0.404 m
Substitute the values above into equation 1
- v = 440(0.404)
- v = 177.76 m/s.
- v ≈ 178 m/s
Hence, The speed of the sound in the xenon is 178 m/s. And the right option is b 178 m/s
Learn more about speed here: brainly.com/question/4931057
