A moving particle

Classical Mechanics Level 3

A particle of mass $\SI{1}{\kilogram}$ is kept at the origin at rest. A force of $F=3xt$ Newton is applied on it. Where $x$ is the x-coordinate of the position of the particle and $t$ is the time elapsed.

Find the time after which it will reach $x= \SI{4}{\meter}.$

3.214 sec 8.122 sec 2.626 sec Infinite

2 solutions

Aarsh Verdhan
Mar 26, 2017

Since at the start x=0 hence the force will remain 0. Hence it will take infiniye time to reach x=4

That was quite tricky

Md Zuhair - 4 years, 2 months ago

Actually it was very difficult to solve with force given as a function of two variable with no relation between them, and intermediate integration womt do it.. Still i named it simple conceptual question. Hence the hint was in the name of the problem itself

Aarsh Verdhan - 4 years, 2 months ago

It would also be fun to make a version of this that has a non-trivial solution, necessitating (I think) the use of a computer.

Steven Chase - 4 years, 2 months ago

@Steven Chase – Yes it would

Aarsh Verdhan - 4 years, 2 months ago

@Aarsh Verdhan – Mind if I go ahead and post it?

Steven Chase - 4 years, 2 months ago

@Steven Chase – No i dont. Go ahead

Aarsh Verdhan - 4 years, 2 months ago

Yes, the second order ODE does get quite tedious. I was going to do Euler integration until I actually sat down and thought about the problem!

Krishna Karthik - 1 year, 1 month ago

It would be nice if somebody on Brilliant took some time and published JEE sets(chapter wise chemistry inclusive). Would be highly helpful to many. Maybe somebody who cracked iit recently or an aspirant would be perfect

Swapnil Vatsal - 4 years, 1 month ago

Krishna Karthik
Apr 21, 2020

I've got to say; this was a fun problem indeed! It did bring a smile to my face when I solved it.

So, the differential equation describing the particle's motion along the $x$ -axis is as follows:

$\ddot{x} = 3xt$

At the initial state, the acceleration of the object is $3\times0\times 0 = 0$

Here's the problem with the motion:

If the particle has an initial velocity of 0, along with the initial acceleration being zero, the object will never move!

Unless there is a non-zero initial value of $\dot{x}$ or $x$ , the solution to the second order ODE above will remain at a steady state, with no change.

So the particle will never reach $x = 4$ given the initial conditions of the differential equation.

A moving particle

2 solutions

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