Force problem in work energy theorem

I have a bit confusion about the term force in general sense. Suppose a body is at rest in the ground, say this to be point A. Then, a force F is applied to it upwards which sends it accelerated against the gravity. Now my confusions are:

1. "In point A, the initial velocity of body is 0. Due to force in upward direction it's velocity will gradually start increasing in upward direction. At point B the velocity will be u1 (say). u1 is greater than 0. Then due to effect of gravity the velocity will decrease again slowly. At point C, the velocity will be u2 (say). u2 will be equal to zero. Then the body will start accelerating downwards under the effect of gravity" - Is the statement correct? If not, please correct me

2. In point A, the force is applied to move the body in upwards direction. Now say at any arbitrary point B, what will be the force acting? Does the question even make sense? I don't know if force will act after the body is punched from the point A in upwards direction.

• The force of gravity is present throughout. It serves to decelerate (negative acceleration) until the object stops moving in the upward direction, and then accelerates the object thereafter. Note that the acceleration doesn't change sign at the apex, it't only the velocity that changes sign. – Lewis Miller Dec 28 '16 at 18:04
• You have to tell us more about the upward force. You say that the velocity gradually increases, then the velocity stops increasing and in fact decreases. This implies that the upward force is changing in time. You have to specify the magnitude of the upward force, and how it behaves with time. – garyp Dec 28 '16 at 18:09

First, it is not really appropriate to say "a force F is applied to it upwards which sends it accelerated against the gravity". The force of the ground is acting on the ball in the opposite direction of the force of gravity - don't talk about acceleration until you have a sum of all the forces acting on the object.

1. The statement is very confusing. What are the forces on the object? If an object is "at rest" on the ground, it will not be moving upwards - it will stay at rest! If you add another force, pointed in the upwards direction, the body may lift off the ground, provided that force is greater than the force of gravity. The further motion you are describing would require this additional force to change over time.

2. The same basic problem is here - you need to know the details of how this force is acting to know anything about it's motion.

I think you might be getting at the following: Consider throwing a ball straight upwards. Gravity will be acting on the ball with a constant force during the entire motion. When I throw the ball, I am acting on it with some force. I want the ball to move upwards, so I act on it with a force larger than gravity. It then leaves my hand, moving upwards. The moment it leaves my hand, I am no longer acting on it so the only force is the force of gravity. The force of gravity causes it to begin to slow down (accelerate in the downwards direction). It continues to rise, but more and more slowly. When it reaches the top of it's arc, it stops momentarily, but the force of gravity makes it move faster and faster downwards until I catch it again (maybe by acting in the opposite way I acted when I threw it).

In order to describe the motion of an object using forces, you have to know each and every force at each and every instant of time.

1. Your statement is correct in case that implies that a force greater than the weight of the body, is acting against gravity during all the time period between points from A to B. Then the force stops acting on the body which now travels with an initial velocity u1 , which is decreasing , until it reaches the maximum height.From that moment and on, the body performs a free fall.

2. I think you are a little bit confused. A force acts on a body for some time $dt$. In this time period it is accelerated according to Newton's second law. I think you must not mix up the terms "force" and "velocity". Try to understand the second law of motion by examining it more carefully.