The velocity at a fixed point in a flow field is given by $2$i $+6$t $$j$.$ Fluid particles passing

through that point continue to move with the velocity they had at that point $($this is

unlikely to happen in real flows$).$

$($a$)$ Draw the pathline of the particle passing through the point at t $=0.$

$($b$)$ Draw the pathline of the particle passing through the point at t $=1.$

$($c$)$ If a dye is injected continuously at this point starting at t $=0,$ what would the dyepattern

look like at t $=3?$ What does this dye$-$pattern represent?