1. A force of 10 N is applied to a 2 kg mass. What is the acceleration of the mass?

Solution:
Using Newton's Second Law of Motion, F = ma, where F is the force applied, m is the mass and a is the acceleration.
So, a = F/m = 10 N / 2 kg = 5 m/s^2

Therefore, the acceleration of the mass is 5 m/s^2.

2. A 5 kg block is pushed with a force of 20 N. What is the acceleration of the block?

Solution:
Using Newton's Second Law of Motion, F = ma, where F is the force applied, m is the mass and a is the acceleration.
So, a = F/m = 20 N / 5 kg = 4 m/s^2

Therefore, the acceleration of the block is 4 m/s^2.

3. A force of 15 N is applied to a 3 kg mass. What is the force required to produce twice the acceleration of the mass?

Solution:
Using Newton's Second Law of Motion, F = ma, where F is the force applied, m is the mass and a is the acceleration.
So, a = F/m

If we want to produce twice the acceleration of the mass, the new acceleration would be 2a.
So, the new force required would be F' = ma' = m(2a) = 3 kg (2 x 15 N / 3 kg) = 30 N.

Therefore, the force required to produce twice the acceleration of the mass is 30 N.

4. A force of 50 N is applied to a 10 kg mass. What is the force required to produce half the acceleration of the mass?

Solution:
Using Newton's Second Law of Motion, F = ma, where F is the force applied, m is the mass and a is the acceleration.
So, a = F/m

If we want to produce half the acceleration of the mass, the new acceleration would be a/2.
So, the new force required would be F' = ma' = m(a/2) = 10 kg (50 N / 2 x 10 kg) = 25 N.

Therefore, the force required to produce half the acceleration of the mass is 25 N.

Force acting on an object is proportional to the rate of change of momentum