# Quick basic kinematics theory

Let's say I throw something up, doesn't matter what it is. But ignore air resistence and other magical stuff going on.

As soon as this object reaches its peak (v = 0) and begins to drop, does the object steadily picks up its speed just as it did when you threw it up? Like does it begin to accelerate at the same rate (downwards) as it did when you throw it upwards?

Because when you throw it up, gravity affects it, but so does your hands?

So the other part i want to get to is, whenever you read problems like "you throw an object up with a speed of....", and you immediately just have gravity in your equation

$$\Delta y = \frac{-gt^2}{2} + v_0 t$$

Is that actually wrong? Because when you throw it up, you actually give an acceleration (hence a force?)

Thanks

jtbell
Mentor
When we say, "you throw an object upwards with a speed of xxx m/s", we really mean "you throw an object upwards, such that at the instant just after it leaves your hand it has a speed of xxx m/s." You begin your kinematics analysis at that instant. Your hand is no longer in contact with the object, and the force that your hand exerts no longer enters into the picture.

When we say, "you throw an object upwards with a speed of xxx m/s", we really mean "you throw an object upwards, such that at the instant just after it leaves your hand it has a speed of xxx m/s." You begin your kinematics analysis at that instant. Your hand is no longer in contact with the object, and the force that your hand exerts no longer enters into the picture.

How does it gain velocity then? If I go by that reasoning, then doesn't that mean I can never give a force? If "just as it leaves my hand, the object gains xxx m/s", feels like it is violating some law...it almost feels like it's in the air for a while and then suddenly jumps up

Doc Al
Mentor
It gains velocity because you pushed it! Your hand exerts a force on the object, accelerating it to some velocity. When it leaves your hand, the only force left acting on it is gravity, so the usual kinematic equations come into play.

How does it gain velocity then? If I go by that reasoning, then doesn't that mean I can never give a force?
Yes, "giving a force" does not make sense in the usual mechanics terminology.
You act with a force and due to this acting the object gains kinetic energy.
The force is not a property of the object, something that the object carries with it. It is a measure of interaction between objects.
Properties that you may say that the object "have" are energy, velocity, acceleration.
The action of a force can change these above quantities of the object.
In your case, when you move your hand upwards, with the object in it, you act with a force (the interaction between object and the moving hand) and as a result the object is accelerated from rest to some velocity. When you let go, the action of the force from the hand stops and the object keeps moving with the velocity it had at that instant. This is your initial velocity for the rest of the problem.

Yes, "giving a force" does not make sense in the usual mechanics terminology.
You act with a force and due to this acting the object gains kinetic energy.
The force is not a property of the object, something that the object carries with it. It is a measure of interaction between objects.
Properties that you may say that the object "have" are energy, velocity, acceleration.
The action of a force can change these above quantities of the object.
In your case, when you move your hand upwards, with the object in it, you act with a force (the interaction between object and the moving hand) and as a result the object is accelerated from rest to some velocity. When you let go, the action of the force from the hand stops and the object keeps moving with the velocity it had at that instant. This is your initial velocity for the rest of the problem.

So when it leaves your fingertips, that's the "initial velocity" (where this "initial velocity" is also the final velocity as it moved from rest in your palm to your fingertips) in most word problems right? That is what you are implying right?

Let's say I throw something up, doesn't matter what it is. But ignore air resistance and other magical stuff going on.

As soon as this object reaches its peak (v = 0) and begins to drop, does the object steadily picks up its speed just as it did when you threw it up? Like does it begin to accelerate at the same rate (downwards) as it did when you throw it upwards?

Because when you throw it up, gravity affects it, but so does your hands?

So the other part i want to get to is, whenever you read problems like "you throw an object up with a speed of....", and you immediately just have gravity in your equation

$$\Delta y = \frac{-gt^2}{2} + v_0 t$$

Is that actually wrong? Because when you throw it up, you actually give an acceleration (hence a force?)

Thanks

yes; you apply a force with your hands in upward direction. But why you go to hands motion if you are desired to finds maximum height, time. If it is asked in question that your hand give a ball velocity of xx m/s to a ball, it moves y meter in upward direction,it's mass is a Kg. then find out the force applied on the ball.Now you will not apply the equation that give you maximum height time etc. Here you will apply kinematics & newton's equation on your hand.(It is assumed that you did not rotate your hand)

You say air resistance a magical stuff. No yar(friend) all this is not magical stuff. Actually working with air friction is too hard for a high school student so they are not placed with kinematics.