Answer:
<em>v = 381 m/s</em>
Explanation:
<u>Linear Speed</u>
The linear speed of the bullet is calculated by the formula:

Where:
x = Distance traveled
t = Time needed to travel x
We are given the distance the bullet travels x=61 cm = 0.61 m. We need to determine the time the bullet took to make the holes between the two disks.
The formula for the angular speed of a rotating object is:

Where θ is the angular displacement and t is the time. Solving for t:

The angular displacement is θ=14°. Converting to radians:

The angular speed is w=1436 rev/min. Converting to rad/s:

Thus the time is:

t = 0.0016 s
Thus the speed of the bullet is:

v = 381 m/s
Answer:
1) 0.43 meters per second
2) 0.21 meters per second
3) 1.02 
4) 0.66 seconds
Explanation:
part 1
By conservation of energy, the maximum kinetic energy (K) of the block is at equilibrium point where the potential energy is zero. So, at the equilibrium kinetic energy is equal to maximum potential energy (U):


With m the mass, v the speed, k the spring constant and xmax the maximum position respect equilibrium position. Solving for v

part 2
Again by conservation of energy we have kinetic energy equal potential energy:


part 3
Acceleration can be find using Newton's second law:

with F the force, m the mass and a the acceleration, but elastic force is -kx, so:


part 4
The period of an oscillator is the time it takes going from one extreme to the other one, that is going form 4.5 cm to -4.5 cm respect the equilibrium position. That period is:

So between 0 and 4.5 cm we have half a period:

When multiple forces are at work on an object, the net force is called a <em>resultant</em>, because it's a sum of vectors, and a sum of vectors is called their resultant.
Given:
v(final velocity)= 7.5 m/s
t(time taken to pedal along)=4.5 s
Displacement (s)=19 m
Now we know that
s=ut+1/2(at^2)
Where s is the displacement measured in m
u is the initial velocity measured in m/sec
a is the acceleration measured in m/s^2.
t is the time taken to cover this distance.
Substituting the given values in the above formula we get
19= 4.5u+1/2(a x 4.5 x 4.5)
20.25 a + 9 u = 38
Now we also know that
v= u + at
Substituting the given values in the above formula we get
7.5= u + 4.5a
Solving for u and a from the above equations we get
u = 0.944m/s
a= 1.45 m/s^2
Thus the initial velocity is 0.944 m/s