Explanation:
S =ut + 1/2at^2
S = 0×6.5 + (1/2 × 9.54) × 6.5^2
S =0 + 4.77 ×42.25
S=201.5m
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:

while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:

And the total energy of the system is

Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:

while the mass is moving at speed v, and therefore the kinetic energy is

And the total energy is

For the law of conservation of energy, the total energy must be conserved, therefore

. So we can write

that we can solve to find an expression for v:
Answer:
236.3 x
C
Explanation:
Given:
B(0)=1.60T and B(t)=-1.60T
No. of turns 'N' =100
cross-sectional area 'A'= 1.2 x
m²
Resistance 'R'= 1.3Ω
According to Faraday's law, the induced emf is given by,
ℰ=-NdΦ/dt
The current given by resistance and induced emf as
I = ℰ/R
I= -NdΦ/dtR
By converting the current to differential form(the time derivative of charge), we get
= -NdΦ/dtR
dq= -N dΦ/R
The change in the flux dФ =Ф(t)-Ф(0)
therefore, dq =
(Ф(0)-Ф(t))
Also, flux is equal to the magnetic field multiplied with the area of the coil
dq = NA(B(0)-B(t))/R
dq= (100)(1.2 x
)(1.6+1.6)/1.3
dq= 236.3 x
C
-- The speed of light in air is very close to 3 x 10⁸ m/s.
Whatever the actual number is, it's equivalent to roughly
7 times around the Earth in 1 second. So for this kind of
problem, you can assume that we see things at the same time
that they happen; don't bother worrying about how long it takes
for the light to reach you.
-- For sound, it's a different story. Sound in air only travels at
about 340 m/s. It takes sound almost 5 seconds to go 1 mile.
-- Now, the lightning and thunder happen at the same time.
The light travels to you at the speed of light, so you see the
lightning pretty much when it happens. But the sound of the
thunder comes poking along at 340 m/s, and arrives AFTER
the sight of the lightning.
The length of time between the sight and the sound is about
99.9999% the result of the time it takes the sound to reach you.
If the thunder arrived at you 3 seconds after the light did, then
the sound traveled
(340 m/s) x (3 s) = 1,020 meters .
(about 0.63 of a mile)
(If you're worried about ignoring the time it takes
for the light to reach you ...
It takes light 0.0000034 second to cover the same 1,020 meters,
so including it in the calculation would not change the answer.)
Answer: 50.7 J
Explanation:
Given
mass of lion is 
The initial speed of the lion is 
increased speed of lion is 
Initially, its kinetic energy is 
Final kinetic energy 
work did by lion after speed up is 
![\Rightarrow W=\dfrac{1}{2}\times 2.6[8^2-5^2]\\\\\Rightarrow W=1.3\times [39]=50.7\ J](https://tex.z-dn.net/?f=%5CRightarrow%20W%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%202.6%5B8%5E2-5%5E2%5D%5C%5C%5C%5C%5CRightarrow%20W%3D1.3%5Ctimes%20%5B39%5D%3D50.7%5C%20J)