2. WORD PROBLEMS 1. The position of a particle at time t is given by s(t) = 10 + 6t - 362. Find the velocity and acceleration of the particle using the limit definition of the derivative. What is the maximum velocity of the particle? What about the maximum speed? What is the particle's speed when s(t) = 0? Sketch a graph of the particle's position (using a computer is fine). Use the graph of position to sketch graphs of velocity and accleratingnot using a computer). 2. Consider the following piecewise function f(x) = x2 -4r +3 xx1 2x' tartb a>1 Find values of a, b so that f is differentiable for all values of r. 1