Motion problem (1 Viewer)

[conman]

The velocity of a body P is given by

Find the value of t when x=pi/4 if P starts from the origin.

 

[pLuvia]

dx/dt=cos²x/(1+sinxcosx)
t=int.(1+sinxcosx)dx/cos²x
=int.sec²x+tanx dx
=tanx-ln(cosx)+C

When t=0, x=0, C=0
t=tan-ln(cosx)
When x=pi/4
t=1-ln(1/sqrt{2})
=1+1/2(ln2)