Motion In A Straight Line

What does negative slope of a position -time graph actually represent?  I mean that it does indicate motion in the opposite direction, but does it also represent the fact that the velocity of the object is decreasing? Also, shouldn't graphs representing motion in an opposite direction start from the origin and move below the x-axis, but I have seen in many graphs that the graph for motion in opposite direction starts from a point above the x-axis?

Please help me clear this doubt regarding negative slopes of graphs.

If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface will be ?

A particle moving in straight line experience constant acceleration for 20 second after starting from rest. If it travel a distance S1 in the first 10 seconds and distane S2 in the next 10 seconds then find the relation between S1 and S2

1. Determine the horizontal velocity u with which a stone must be projected from point p of height h so that it may hit the inclined plane perpendicularly. Inclination is theta and inclined plane is kept just below point p at ground. Give the value in terms of g, h and cot theta.                                                                                                                                                                                                                                                                                             2. Point A moves uniformly with velocity v so that vector v is continually aimed at point B which in its turn moves rectilinearly with velocity u<v. Initially, u perpendicular to v and separation was l. How soon will the points converge.     Plz answer both the questions as I have exam tommorow.

A student goes from his house to his friend's house with speed v1. Finding the door of his friend's closed,return back to his own house with the speed v2. Then the average speed of the student is 

The velocity of a particle moving on the x-axis is given by v=x^2+x, where x is in m and v is in m/s. What is its position when its acceleration is 30 m/s^2

a small ball is dropped from a height h onto a rigid frictionless plate at b and rebounds find the maximum height reached after rebound if the coffecient of restitution between the ball and the plate is e=0.75

A particle starts from rest and traverses a distance l with uniform acceleration, then moves uniformly over a further distance 2l and finally comes to rest after moving a further distance 3l under uniform retardation. Assuming entire motion to be rectilinear motion, the ration of average speed over the journey to the maximum speed on its way is: