Question

Water flows through a pipe with a velocity given by V⃗ = (4/t + x + y) ĵ m/s, where ĵ is the unit vector in the y-direction, t(>0) is in seconds, and x,y are in meters. The magnitude of total acceleration at the point (x,y)=(1,1) at t=2s is ___ m/s².

Accepted Answer

The correct answer is 3 m/s² (± 0.5). Since velocity has only a y-component v=4/t+x+y (u=0), the x-acceleration is zero. The y-acceleration is the material derivative: a_y = ∂v/∂t + u∂v/∂x + v∂v/∂y = −4/t² + 0 + v(1). At t=2,x=1,y=1: v=4/2+1+1=4, so a_y = −4/4 + 4 = 3 m/s². Total acceleration magnitude = 3 m/s².

Explanation