# [Physics] An upward force against gravity

forcesnewtonian-gravitynewtonian-mechanics

If two forces are applied against each other,we can simply sove it by subtraction.But what if a force is constantly applied while the other is not?For example,when I throw a ball upwards,I applied a force upwards against the gravitational force,how do we calculate the initial velocity of the ball and if the force applied is greater than the gravitational force on the first moment,how do I know the changes in the acceleration of the ball?It would be best if you can provide me an example.
(I have learnt the basic formula such as v^2=u^2+2as but most of them did not tell regarding this type of situation.）

For example,when I throw a ball upwards,I applied a force upwards against the gravitational force,how do we calculate the initial velocity of the ball

Gravity applies it's force all the time. But you apply a force for as long as you are still touching the ball. As soon as you let it go, it continues upwards with its initial velocity, that you have given it by accelerating it upwards, and trek only gravity works during the flight. So it slows down.

It all comes down to the total force that the object feels. Newton's 2nd law says this.

$$\sum F=ma$$

During the flight, it only feels gravity. So it only feels a force downwards. So it accelerates downwards. So it slows down.

During the throw while you are still in contact with the object, it feels gravity downwards but also you force upwards. If you force is largest, then it accelerates upwards. So it speeds up upwards. Which speed it then reaches at the end of your throw just before you don't touch it any more, depends on for how long you applied your throwing force.

if the force applied is greater than the gravitational force on the first moment,how do I know the changes in the acceleration of the ball?

You know the acceleration from Newton's 2nd law above. You just have to know the throwing force which you are applying.