Infinitely Moving Object

Classical Mechanics Level 3

If an object is placed at position = 1 m =1 \text m and starts moving with velocity 1 m/s 1 \text{m/s} , acceleration 1 m/s 2 1 \text{m/s}^2 , jerk 1 m/s 3 1 \text{m/s}^3 , all the way up to infinity, what will its position be after exactly one second, in meters?

π e √2 φ

Maurice Pierre by Maurice Pierre , 22, USA

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1 solution

In order for d n x ( t ) d t n = 1 \dfrac{d^{n}x(t)}{dt^{n}} = 1 at t = 0 t = 0 for all non-negative integers n n we will require that

x ( t ) = 1 + t + t 2 2 ! + t 3 3 ! + t 4 4 ! + . . . . = e t . x(t) = 1 + t + \dfrac{t^{2}}{2!} + \dfrac{t^{3}}{3!} + \dfrac{t^{4}}{4!} + .... = e^{t}.

Thus its position ( in meters) at t = 1 t = 1 is x ( 1 ) = e . x(1) = \boxed{e}.

15 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for the solution! Help me share this problem!

Maurice Pierre - 6 years, 2 months ago

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I'd never imagine creating a problem like this! Nice one!

Jake Lai - 6 years, 2 months ago

Nice problem. I have reshared it. :)

Brian Charlesworth - 6 years, 2 months ago

Thanks for the problem. It was Brilliant.

Rishav Koirala - 6 years, 2 months ago

Why can we use r=ro+v(t)+1/2at^2+1/6(jerk)t^3 ??? with t=1s?

Dylan Scupin-Dursema - 6 years, 1 month ago

didn't understand your question, can you elaborate ?

Rohan Joshi - 4 months, 1 week ago

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