1. The problem statement, all variables and given/known data The accompanying graph of position x versus time t represents the motion of a particle. If p and q are both positive constants, the expression that best describes the acceleration of the particle is 2. Relevant equations (A) a = - p - qt (B) a = p + qt (C) a = p + qt (D) a = p - qt 3. The attempt at a solution In a given solution (D) is the correct answer. But if we integrate the differential eq obtained from a = p-qt , we get velocity v = pt -0.5qt^2+c the value of v ie dx/dt =0 for the inflexion pts on x vs t curve and we can get two values of t of the quadratic equation qt^2 -2pt -2c =0 but this gives one negative value of t which is impossible. Then is (D) option correct? what is my wrong approach ?