Water flows though a pipe with a velocity given by V→

Water flows though a pipe with a velocity given by V^→ = 4 + x + y ĵ m/s
t

m/s, where ĵ is the unit vector in the y direction, t(>0) is in seconds, and x and y are in meters. The magnitude of total acceleration at the point (x, y) = (1, 1) at t = 2 s is _____ m/s².

Given:

V =		4	+ x + y		ĵ m/s
		t

V = uî + vĵ + wk̂
u = 0, w = 0

V =		4	+ x + y		ĵ
		t

a = a_xî + a_yĵ + a_zk̂

a_x = u	∂u	+ v	∂u	+ w	∂u	+	∂u	= 0
	∂x		∂y		∂z		∂t

a_z = u	∂w	+ v	∂w	+ w	∂w	+	∂w
	∂x		∂y		∂z		∂t

a_y = u	∂v	+ v	∂v	+ w	∂v	+	∂v
	∂x		∂y		∂z		∂t

= u	∂v	+ v	∂v
	∂y		∂t

=		4	+ x + y		× 1 +		4
		t					t²

a_y =		4	+ x + y −	4		ĵ
		t		t²

Now, At (x,y) = 1,1 and t = 2 sec.
Total acceleration is given by,

a = a_y =		4	+ 1 + 1 −	4		= 3 m/s²
		2		4