IIT JEE , AIEEE Forum - Physics , Mechanics

rakesh61

What determines the nature of the path followed by a particle

a) speed

b) velocity

c) acceleration

d) none of these

Ans given is d

Please explain with correct reason (AFMC 2005) qns

spideyunlimited

there's magnus effect too (swinging of cricket balls), streamlining etc... thats what they mean most probably.

kundan_leo

i cant be precised about this..............
but i remember reading an article of neil bohr and his experiments........
and it was his theory that was induced in modern physics........

he said that the nature of particle motion can only be explained by quantum physics..
you know relation between energy(quanta) and matter......

and the rest of options are variable in various cases.......
that's why its d

feynmann

velocity

It indicates the instantaneous direction of motion .

elessar_iitkgp

To know the nature of the path of the particle we must know the law of variation of position vector with time, for the path is but the locus of the end point of the position vector
If you are given velocity, then
dr/dt = v
_r0

^r dr = _t0

^t vdt
r = r₀ + _t0

^t vdt
where r₀ is the position vector of the particle at time t. , ie, r₀= r(t₀)
Now, until and unless r₀ is given, you can't determine r. So with velocity alone, the law of variation of position vector can't be found. Its position vector at a certain instant t₀ must be known before hand.

Similar remarks apply to acceleration. If you start integrating from a then you will need the velocity v₀ at certain time t₀ as well as the position vector r₀ at that time.

Hence the option (D) is correct

@feynamnn,
The nature of the path can only be analyzed if you have the equation of the curve in any coordinate form .Most commonly its the Cartesian Coordinate form, ie, once you know the function r = r(t), you can generate three equations of the form
x = x(t)
y=y(t)
z=z(t)
Eliminate t from these three and you get the equation of the path. From this equation you can then analyze the nature of the path, ie, intervals of increse/decrease, curvature and all sorts of things

Similar remarks apply for any other coordinate system such as plane polar, spherical polar, cylindrical polar, or a generalized coordinate system.

@viv
Yes, ultimately it is the force applied that governs the path. It is apparent once you start from acceleration as acceleration itself is caused by force.

Given the position r, one can determine the velocity v and acceleration a of the particle without any further information using
v = dr/dt
a=dv/dt
However, the three kinematics equation are just the solution to the reverse problem:
"To find the velocity and position of a particle if the acceleration is given"
One can extend this to
"To find the velocity and position of a particle if the force acting on the particle is given"
Now, it turns out that the solutions to this problem requires two initial conditions, namely, the position and velocity at a certain moment of time t₀, ie, v₀ and r₀

feynmann

Hey it asks for the NATURE of the path . Not the actual one!!!!!!

VIV

THIS IS A THOUGHT PROVOKING QUESTION.

THE NATURE OF PATH IS PERHAPS DETERMINED BY ITS EQUATION.
FOR E.G. IN A STRAIGHT LINE PATH THE EQUATION WILL BE
Y=mX+C

IN PARABOLA,IT CAN BE:Y²=4*a*X ETC.

NOW A NATURAL QUESTION ARISES,WHAT DETERMINES THESE EQUATIONS?
I SUPPOSE THAT THESE ARE DETERMINED BY :

1.)THE DIRECTION OF THE NET (RESTORING) FORCE OR TORQUE (INTERNAL + EXTERNAL) ACTING ON THAT SYSTEM.
2.)angle of contact(not always)(for eg in game of carrom it is the angle between the striker and the carrom men that decides the nature of path)

(D) IS CORRECT CHOICE.

PLEASE COMMENT.

VIV

SORRY,' ELESSAR_IITKGP'
I DID NOT KNOW THAT YOU HAVE ALREADY POSTED THE ANSWER.

deeplove

the motion is caused by force. FORCE gives acceleration and thats the region of all other mechanical things.. so i think its acceleration.

amitp91

i think the wve nature of the particle will actualy decide the nature of the path . but since it is not in the option the nearest answer is acceleraTION

amitp91

i think the wve nature of the particle will actualy decide the nature of the path . but since it is not in the option the nearest answer is acceleraTION

spideyunlimited

@every1
i already throught of wht u said, plz consider the point i made

hsbhatt

How about: the frame of reference of the observer

akhil_o

I believe its the direction of the acceleration vectors and the angle it makes with the velocity....and in the options they mean the magnitude of v and a which does not help to detrmine nature

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