Physics > Motion in One Dimension > 6.0 Analysis of motion through graph
Motion in One Dimension
1.0 Introduction
2.0 Kinematic variables
2.1 Distance and displacement
2.2 Average speed and velocity
2.3 Instantaneous speed and velocity
2.4 Average and instantaneous acceleration
3.0 Motion in one dimension
3.1 Motion in a straight line with uniform velocity
3.2 Motion in a straight line with uniform acceleration
3.3 Motion in a straight line with non-uniform acceleration
4.0 Derivation of the kinematics equation
5.0 Vertical motion under gravity
5.1 Basic terminologies for motion under gravity
5.2 Detailed concept of motion under gravity
5.3 Solved examples
6.0 Analysis of motion through graph
6.1 Displacement - time graph
6.2 Velocity - time graph
6.3 Area under the graph
6.4 Solved examples
7.0 Relative motion
7.1 Relative displacement
7.2 Relative velocity
7.3 Relative acceleration
7.4 Illustration of relative motion
7.5 Application of relative motion
8.0 Simultaneous motion of two bodies
9.0 River boat problem
9.1 Downstream
9.2 Upstream
9.3 Crosses the river in shortest interval of time
9.4 Reaches the point just opposite from where he started
9.5 River-man problem
9.6 Solved examples
10.0 Aircraft-wind problem
11.0 Rain problem
6.2 Velocity - time graph
2.2 Average speed and velocity
2.3 Instantaneous speed and velocity
2.4 Average and instantaneous acceleration
3.2 Motion in a straight line with uniform acceleration
3.3 Motion in a straight line with non-uniform acceleration
5.2 Detailed concept of motion under gravity
5.3 Solved examples
6.2 Velocity - time graph
6.3 Area under the graph
6.4 Solved examples
7.2 Relative velocity
7.3 Relative acceleration
7.4 Illustration of relative motion
7.5 Application of relative motion
9.2 Upstream
9.3 Crosses the river in shortest interval of time
9.4 Reaches the point just opposite from where he started
9.5 River-man problem
9.6 Solved examples
As we know, $$\frac{{ds}}{{dt}} = v$$ and $$\frac{{{d^2}s}}{{d{t^2}}} = a$$
| S. No. | Type of motion | Graph | Explanation |
1. | Uniform motion |
| As slope is parallel to the time axis. So, $$\frac{{dv}}{{dt}} = 0$$or$$a = 0$$ |
2. | Uniformly accelerated motion |
| As slope is constant. So, $$a = \frac{{dv}}{{dt}} = + ve$$$$a = {\text{constant}}$$ Slope is $+ve$ as it makes actue angle with $x-$axis. Therefore, velocity increases with time. |
3. | Uniformly retarded motion |
| As slope is constant. So, $$a = \frac{{dv}}{{dt}} = - ve$$$$a = {\text{constant}}$$ Slope is $-ve$ as it makes obtuse angle with $x-$axis. Therefore, velocity decreases with time. |
