Calculus question

Question 5 (a) Apply differentiation to calculate the equation of the tangent to the function f (x) = x2 at the point (3,5). [6 Marks] (b) The position of a particle in an engineering system is given by the following equation: t 2 s (t) = 5t + t+ 1 Where s(t) is the position of the particle at time t (m), and t is the time (seconds) (i) Calculate the velocity of the particle at t = 10 sec [6 Marks] (ii) Calculate the acceleration of the particle at t = 10 sec [6 Marks] (iii) Calculate the time at which the particle is at rest [2 Marks]