(a) 6.04 rev/s
The speed of the ball is given by:

where
is the angular speed
r is the distance of the ball from the centre of the circle
In situation 1), we have

r = 0.600 m
So the speed of the ball is

In situation 2), we have

r = 0.900 m
So the speed of the ball is

So, the ball has greater speed when rotating at 6.04 rev/s.
(b) 
The centripetal acceleration of the ball is given by

where
v is the speed
r is the distance of the ball from the centre of the trajectory
For situation 1),
v = 30.6 m/s
r = 0.600 m
So the centripetal acceleration is

(c) 
For situation 2 we have
v = 34.1 m/s
r = 0.900 m
So the centripetal acceleration is

Answer:
0.372 kg
Explanation:
The collision between the bullet and the block is inelastic, so only the total momentum of the system is conserved. So we can write:
(1)
where
is the mass of the bullet
is the initial velocity of the bullet
is the mass of the block
is the velocity at which the bullet and the block travels after the collision
We also know that the block is attached to a spring, and that the surface over which the block slides after the collision is frictionless. This means that the energy is conserved: so, the total kinetic energy of the block+bullet system just after the collision will entirely convert into elastic potential energy of the spring when the system comes to rest. So we can write
(2)
where
k = 205 N/m is the spring constant
x = 35.0 cm = 0.35 m is the compression of the spring
From eq(1) we get

And substituting into eq(2), we can solve to find the mass of the block:

Answer:
The answer to your question is: C. -9.81 m/s²
Explanation:
A. 9.81 m/s² acceleration is considered positive when it goes to the center of the earth, so this option is incorrect.
B. 0 m/s² This option is incorrect because acceleration is 0 for a linear motion without acceleration.
C. -9.81 m/s² If a projectile goes to the sky, then the acceleration will be negative.
D. It is not constant. Acceleration is constant.
There's the acceleration of the car that provides a force and the normal force of the seat cushion which pushes upwards against the passenger