Equation of motion by graphical methods

 

(i)   Distance -Time Graph

•    Distance – Time Graphs represents a change in position of the object with respect to                  time. The graph in case the object is stationary  (means the  distance is constant at all                time intervals) – Straight line graph parallel to x = axis
•    For a distance-time graph, time is taken on x-axis and distance is taken on the y-axis.
•    For a body at rest, as the slope is zero, so the speed of the body is zero
•    For a body moving with uniform speed
•    For an accelerated motion., the slope of the graph is increasing with time
•    For decelerated (speeding down) motion, the slope of the graph is decreasing with time.

(ii) Velocity- Time Graph

•    Constant velocity is a straight-line graph, velocity is always parallel to the x-axis. When a        body is moving with a uniform velocity, the slope of AB indicates zero acceleration.
•    When a body starts from rest and moves with uniform acceleration, then it is greater is the        slope of the v-t graph, greater will be the acceleration.
•    When a body is moving with uniform acceleration and its initial velocity is not zero.
•    When a body is moving with increasing acceleration, the slope gradually increases with            time.

 


•    When a body is moving with decreasing acceleration, the slope decreases with time.
•    When a body is moving with uniform retardation and its initial velocity is not zero, as θ > 90°, the               graph has a negative slope.

                                              Derivations

(i)velocity-time relation:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(ii)  Position-time relation:

 

 

 

 

 

 

 

 

 

 

(iii) Position-velocity relation:

 

 

 

 

 

 

 

 

 

 

 

Uniform circular motion

When a body moves in a circular path with uniform speed, its motion is called uniform circular motion.