Question

a particle moving in the xy plane has velocity components dx/dt =2t and dy/dt = 4. If the particle starts from the origin at t = 0,magnitude of its displacement at t=2 is

Answer 1

dx/dt=2t, integrate, x=t^2+Cx
dy/dt=4, integrate, y=4t+Cy

We know x(0)=y(0)=0 => Cx=Cy=0

The trajectory of the particle is therefore
<t^2, 4t>

Guess you can find displacement at t=2 with the above information.