16 6. A physics student is studying the movement of particles in an electric field. In one experiment, the distances in micrometres of two moving particles, A and B, from a fixed point O are modelled by d t d t t A B = − = − + 5 31 3 25 8 2 respectively, where t is the time in seconds after motion begins. (a) Use algebra to find the range of time for which particle A is further away from O than particle B is from O. (8) It was recorded that the distance of particle B from O was less than the distance of particle A from O for approximately 4 seconds. (b) Use this information to assess the validity of the model. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________