Displacement – Time graph:

When a body is thrown vertically upward, within a time t sec the ball reaches the maximum point and then begins to fall. Hence, the displacement – time graph indicates the upward movement of the ball along the Y – axis. As time in the X – axis increases, the upward movement in Y- axis increases and reaches the maximum point.

After this, due to gravity the object will fall which is indicated by the dotted lines. We assume that the only force acting on an object is the force of gravity which causes it to accelerate towards the center of the Earth at a constant rate of 9.8 m/s². We refer the motion to the vertical y axis with +y vertically up.

AB in the diagram indicates displacement time graph for an object thrown upwards and BC indicates velocity time graph for an object coming down from maximum height.

Velocity – Time graph:

When an object moves up against force of gravitation, acceleration is negative. When an object falls down, acceleration is positive.

We know that if y is displacement, dy/dt is velocity and d²y / dt² is acceleration. The slope of the velocity-time graph gives the acceleration.

For a object thrown upwards, we expect a negative slop. Also, at a time when the object reaches maximum height, dy/dt should be zero. Hence, the graph is as shown.

PQ in the diagram indicates velocity time graph for an object thrown upwards and QR indicates velocity time graph for an object coming down from maximum height.