A particle A moves in one direction along a given trajectory with a tangential acceleration w_tau=atau, where a is a constant vector coinciding in direction with the x axis(figure), and tau is a unit vector coinciding in direction with the velocity vector at a given point. Find how the velocity of the particle depends on x provided that its velocity is negligible at the point x=0.

A particle A moves in one direction along a given trajectory with a ta

1.	A particle A moves in one direction along a given trajectory with a tangential acceleration w_tau=atau, where a is a constant vector coinciding in direction with the x axis(figure), and tau is a unit vector coinciding in direction with the velocity vector at a given point. Find how the velocity of the particle depends on x provided that its velocity is negligible at the point x=0.
Answer» Solution :In accordance with the problem `w_t=vecavectau` But `w_t=(vdv)/(DS)` or `vdv=w_tds` So, `vdv=(vecavectau)ds=vecadvecr` or, `vdv=avecidvecr=adx` (because `veca` is DIRECTED towards the X-axis) So, `underset0oversetvintdv=aunderset(0)overset(x)intdx` Hence `v^2=2ax` or, `v=sqrt(2ax)`

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