Abody of mass m moves in a horizontal direction such that at time t its position is given byx(t)=at4+bt3+ct, where a, b, and c are constants. (a) what is the acceleration of the body? (b) what is the time-dependent force acting on the body?

The acceleration is given by de second derivative of x(t) which is equal to m/s^2

Explanation:

a) We have the equation x(t)=at^4+bt^3+ct which is the position of the body of mass m at a time t

Where a, b and c are constants

From the rules of differenciation we have that the first derivative of the position is the velocity  and the second derivative is the acceleration.

Hence the first derivative of the function is equal to [/tex] m/s

Don´t forget to write down the unities

Then we have to derivate again this equation, so we have

m/s^2" alt="\frac{d^{2}f(x) }{d^{2}x }=12at^{2} + 6bt" /> m/s^2" />

b) Remembering the Newton´s laws we know that

where:

F is the force

m is the mass

and a is the acceleration

From the first part we know the value of the acceleration which is

m/s^2

So using the second law formula and replacing the values we have that

F=m( ) N

Remember the that N= Newton which is kg*m/s^2

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40

b.

hope this : )