# Problems: Motion in Two dimensions including projectile motion

- A particle moving in the xy-plane has velocity components dx/dt = 6 + 2t and dy/dt = 4 + t

where x and y are measured in metres and t in seconds.

(i) Integrate the above equation to obtain x and y as functions of time, given

that the particle was initially at the origin.

(ii) Write the velocity v of the particle in terms of the unit vectors ˆi and ˆj . - (iii) Show that the acceleration of the particle may be written as a = 2ˆi + ˆj .
- (v) Find the magnitude of the acceleration and its direction with respect to the x-axis.