A speeder traveling at a constant speed of 109 km/h races past a billboard. A patrol car pursues from rest with constant acceleration of (8 km/h)/s until it reaches its maximum speed of 143 km/h, which it maintains until it catches up with the speeder. How long does it take the patrol car to catch the speeder if it starts moving just as the speeder passes

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".