3 A particle Q of mass \(m\) moves in a horizontal plane under the action of a single force \(\mathbf { F }\). At time \(t , \mathrm { Q }\) has velocity \(\binom { 2 } { 3 t - 2 }\).
- Find an expression for \(\mathbf { F }\) in terms of \(m\).
At time \(t\), the displacement of Q is given by \(\mathbf { r } = \binom { x } { y }\). When \(t = 1 , \mathrm { Q }\) is at the point with position vector \(\binom { 4 } { - 4 }\).
- Find the equation of the path of Q , giving your answer in the form \(y = a x ^ { 2 } + b x + c\), where \(a\), \(b\) and \(c\) are constants to be determined.
- What can you deduce about the path of Q from the value of the constant \(c\) you found in part (b)?