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.