Looking for help understanding how I might calculate telekinetic strength in my story

So I have a character in a story that is just about to gain telekinetic powers. The strength of his telekinesis will vary from circumstance to circumstance and time to time, changing often.

I’ve been rating his telekinetic strength by how much mass he can suspend against Earth’s gravity. So, for example, when he begins he is limited to an amount of TK strength equal to keeping 5 pounds afloat in mid-air, but later his power will allow him to float 50 pounds, 500 pounds, or even more, depending.

A couple of other notes about how his TK works: it simply adds the desired force to an object without requiring any equal but opposite reaction – yes, we’re breaking that law. Also, with enough power he can use it on himself to make himself float, or even fly. (Since he weighs 250 pounds, he will obviously only be able to do this when his TK strength is high enough.)

I have many questions I want to answer about his use of TK at different strengths (rated by how much mass he can suspend against Earth’s gravity), mostly boiling down to how to calculate the motions he can cause or stop at his various strengths. Such as:

If his TK is currently at a strength of 5 pounds (meaning enough to keep a 5 pound weight suspended in mid-air), how do I answer the following questions:

If a 3-pound ball is on the ground, how fast and far can he “kick” it using a momentary application of his TK?

If a 3-pound ball is on the ground, and he applies his full force to it continuously (not as an impulse “kick”) over time, how fast and far is it after 10 seconds? After one minute?

If a 3-pound ball is in his hand, how far and fast can he “throw” it (without it rolling it, i.e. it stops when it hits the ground) using a momentary application of his TK? Assuming he uses the optimum angle of launch?

If a 3-pound ball is in his hand, and he applies his full force to it in a straight line continuously over time (and not as an impulse “throw”), how fast and far is it after 10 seconds? After one minute? Once he stops impelling it, how far can it wind up (without rolling, i.e. it stops when it hits the ground)?

What if instead he moves this ball in a 10-foot diameter orbit around his head through the air, how fast can he make it move?

And now, what if he gains more TK strength, how does having 50 pounds of TK strength change the answers above, or 500 pounds of strength? Or what if the ball were a 10-pound ball, or 100 pounds?

Obviously, I am looking here to learn not just the answers to these questions, but what I would have to do to calculate these answers as the factors change.

For that matter, how do I calculate how much TK strength he would need to stop a bullet? Or a car travelling at 60 mph? How fast can he fly with 250 pounds of weight, given his current TK strength of X? What if he’s flying himself and his friends, 1000 pounds of weight?

When I try to figure these things out I get lost very quickly. For example, I know that to suspend himself in mid-air he would need a TK strength of 250 pounds, because that’s what he weighs. But I have no idea how to figure out how much TK strength he would need to fly at 100 mph.

How do I begin to use formulae to calculate these things given a known current TK strength of X, measured in the pounds he can suspend against Earth’s gravity?

PS: Although this may seem like a topic better suited for a science group, the reactionless nature of the ability makes it a non-starter there.

Thanks.

If we say that this character's telekinesis (henceforth TK) simply applies a force to an object... and Force = Mass x Acceleration, or F=MA.

I prefer working in SI units, so I'll use those in this answer, but units don't really make much difference, save for conversion.

So, if the character's TK can support 5 kg against gravity, then the TK is exerting a force of about 50 newtons ($50 kgms^{-2}$), if we approximate gravity to be 10 m/s^2.

The 'momentary kick' of a 3kg ball on a flat surface with 50N of force will accelerate the ball... how much depends upon how long, but the acceleration is calculated with good old F=MA. We know F: 50N, and we know M: 3kg, so to solve for A, we have A= F/M. 50/3 = 16.67 m/s^2 acceleration.

To get speed from constant acceleration and time, from rest, we have Speed = Acceleration x Time., or If we assume a 1 second, 50N, 16.67 m/s^2 kick, then the 3kg ball will be moving 16.67 m/s. If the kick is only 0.1s, then it'll be moving at 1.667m/s. If it's 10s, it'll be 166.7m/s, and if it's 60s, it'll be 1000m/s... if it's in a vacuum.

The problem with working with spherical objects in a vacuum is that we're not typically in one or dealing with spheres. There's usually air around, and air imposes drag upon objects that move through it.

If we're throwing things, then that's a matter of ballistics... where drag also applies if there's an atmosphere.

To calculate how far something goes when it's under uniform acceleration, that's just a matter of displacement, and the Wikipedia article on uniform acceleration covers that too. However, once TK gets something moving, inertia is going to keep it moving... it's not just going to stop because there is no telekinetic force any more, it'll take drag and/or an obstacle to do that.

Propelling a ball in a circle is an application of centripetal force, where Acceleration = Velocity^2/Radius, and F=MA again, so here F = Mass x (Velocity^2/Radius). Just plug in the numbers and do some algebra if necessary to solve for what you're after.

So if this character's TK becomes stronger, it's just applying more Force.

Things like stopping a bullet or a car is just a matter of providing a counter-force over a sufficient time. As long as you know the mass and velocity of the object, and the force the TK can apply, you can work out how long it'll take, and how far it'll travel before it stops.

Flying is the same as throwing something... the character is pretty much throwing himself. Just factor in velocity and drag forces (and whether he's flying superman-style or face-first, it'll make a difference), and you can work out how much force is required. If the character is holding himself up and pushing himself along rather than just becoming ballistic, deduct the force required to hold him aloft from the force that's pushing him along. If the maximum force he can apply is just enough to lift him against gravity, he isn't going to have any to spare for lateral movement.

To work out just how fast this TK-using flier can fly, look up Speed Skydiving and substitute telekinetic forces for gravity... the rest of the calculations and constants are very relevant.

If you want to do calculations on forces and the resulting accelerations and speed you should start taking lessons in the topic of kinetic or read a bit about it. But here something to get you started with the most basic formular

Force (in N) equals mass (in kg) times acceleration (in m/s²).

The gravitational acceleration is roughly 9.81 m/s² 5 pounds equal roughly 2.27 kg so to levitate a 5 pound object you would need at least generate a force of: 2.27 * 9.81 = 22.3 Newtons. However that would only suffice to levitate it. To lift it you need a slight bit more depending on how fast you want to lift it.

Now for acceleration of a 3 pound object you can take that formular again: F = m * a a = F/m a = 22.3 / 1.36 = 16.4 m/s²

So your Character could accelerate a 3 pound object by 16.4m/s for every second he applies his power. Formular: v (speed) = a (acceleration) * t (time over which the acceleration is applied)

This ofcourse neglects air resistance, which makes calculations much more complicated.

On the topic of bullets

Other answers have already covered the general premise, so I’d like to address the “stopping bullets” part specifically.

If we assume a standard 9mm handgun, we have a muzzle velocity of ~250m/s and a bullet mass of 0.007kg.

To stop that bullet at a range of 10 meters means the force needs to be applied over a roughly 0.04 second period. That means you need to decelerate the bullet at ~6250m/s^2. Using F=ma that gives a force required of ~45N. This is about as much force as it takes to levitate a 10 pound object.

Similar calculations for a NATO 5.56 round come out to ~1250N, which is the force needed to levitate a 130 pound object.

Of course you’ll need to be able to react within 0.01-0.04 seconds, which won’t be possible with regular human reflexes.