Speed and velocity

Acceleration

Acceleration is defined as rate of change of velocity.

Linear motion equations

v=u+at                                                                                                                                                                           S=ut+½at²                                                                                                                                                                 v²=u²+2as                                                                                                                                                                   S=½(v+u)/t

Displacement vs Time graph

Gradient of a displacement vs time graph gives  velocity.

There are several types of displacement time graphs. Every displacement time graph represents the nature of motion of the body.

gradient = 0 m/s so velocity = 0 m/s

For a body moving with non-uniform velocity means that the displacement of the body covers in equal of interval of time is increasing, then the displacement time graph is a curved line tells that the velocity is increasing.

If we draw the tangent at several points on the graph, we observe that as the time increases the slope of the tangent also increases. Increasing slope shows that the velocity is not uniform and the motion is accelerated.

For a body moving with non-uniform velocity means that the displacement of the body covers in equal of interval of time is decreasing, then the displacement time graph is a curved line tells that the velocity is decreasing.

If we draw the tangent at several points on the graph we could see that as the time increases the slope of the tangent decreases. Decreasing slope shows that the velocity is not uniform and the motion is retarded.

 The negative gradient indicates it is moving in the opposite direction (moving ‘backwards’) – so it finishes up where it started

Velocity vs Time graph

Gradient of a velocity-time graph gives acceleration.                                                                                              Area under v-t graph gives displacement.

   Uniform velocity

Positive Velocity Zero Acceleration	Positive Velocity Positive Acceleration

                                                                                                                         Accelerating                     Decelerating

Acceleration vs Time graph

Area=at=v-u=change in velocity