A particle of mass 4 kg moves in a plane under the action of three forces (6i−2j)(6\mathbf{i}-2\mathbf{j})(6i−2j) N, (pi+8j)(p\mathbf{i}+8\mathbf{j})(pi+8j) N and (2i−qj)(2\mathbf{i}-q\mathbf{j})(2i−qj) N.
The acceleration of the particle has magnitude 2.5 m s−2^{-2}−2 and is parallel to 3i+4j3\mathbf{i}+4\mathbf{j}3i+4j in the same direction.
Determine the values of the constants p p\,p and qqq.