anyone can help me with this question would be greatly appreciated.

the velocity of a particle after time t is given by v=t^2 + 3. prove that the particle never returns to its original position.

the velocity of a particle after time t is given by v=t^2 + 3. prove that the particle never returns to its original position.

Original post by J4mi3Mike

anyone can help me with this question would be greatly appreciated.

the velocity of a particle after time t is given by v=t^2 + 3. prove that the particle never returns to its original position.

the velocity of a particle after time t is given by v=t^2 + 3. prove that the particle never returns to its original position.

Is it really a proof by contradiction? What do you notice about the velocity (sketch it?) and what will then happen when you integrate it to get displacement.

What mqb says.

For presentation sake, you probably want your first line to be "assume, towards a contradiction, that the particle returns to its original position."

Then do the integration and such, and find the absurdity.

Though do you need to? Uh... if you want to make your teacher happy...

If you can choose not to do the maths, you can note that the particle's velocity at any given time t is non-negative (f'(t)>=0...) and thus the particle's displacement is increasing (...implies f(t) is increasing). Or in other words, the particle never travels backwards.

For presentation sake, you probably want your first line to be "assume, towards a contradiction, that the particle returns to its original position."

Then do the integration and such, and find the absurdity.

Though do you need to? Uh... if you want to make your teacher happy...

If you can choose not to do the maths, you can note that the particle's velocity at any given time t is non-negative (f'(t)>=0...) and thus the particle's displacement is increasing (...implies f(t) is increasing). Or in other words, the particle never travels backwards.

(edited 9 months ago)

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