Graphs of Motion- Types of Motion Graphs

Graphs of Motion 

Explanation: 

Introduction to the graphs: 

Generally, graphs are plotted between two variables, one is the independent variable, and another is the dependent variable 

Let’s say x is an independent variable and y is the dependent variable. If a graph is plotted between x and y (x,y), the following points should be remembered before plotting a graph. 

Points to be remembered: 

1. An equation between C 

2. If the graph is passing through the origin, then x=0 and also y=0. Suppose no graph is passing through the origin. 

3. Differentiating y with respect to x can give the slope of the graph at that point. 

4. To find out the area covered in the graph, integrate y along the x-axis. 

5. Most asked graphs in motion are (s-t,v-t,a-t and v-s). 

Graphs of uniform motion: 

The equations which appear in uniform motion graphs are  

a=0,v = const, s=vt or s=s₀ + vt 

 Important points to remember: 

1. St graph is linear, hence it is a straight line. 

2. As v is constant, then the slope of the curve is constant. 

3. As a=0, then the slope of the curve is zero. 

4. S=vt graph starts from the origin.  

5. s=s₀ + vt graph may or may not start from the origin as displacement can be taken from any point on the graph. 

Graphs of uniformly accelerated motion: 

Generally, we encounter following equations in graphs of uniformly accelerated motion: 

a = 0(positive) 

v=u+at or v=at 

s=ut+1/2at² or s=1/2at² 

s=s₀+ut+1/2at²  or s₌s₀+1/2at² 

Important points to remember: 

1. v-t is a straight line as it is linear in the graph. 

2. s-t is a parabola as all the s-t equations are quadratic in the graph. 

3. The slope of the s-t graph gives instantaneous velocity. As instantaneous velocity is positive and constantly increasing, the graph s-t is also positive and constantly increasing. 

4. The slope of the v-t graph gives instantaneous acceleration, which is positive and increasing.  

Graphs of uniformly retarded motion: 

We encounter following equations using graphs of uniformly retarded motion 

a=constant(negative) 

v=u-at 

s=ut-1/2at² 

Important motion: 

1. The v-t graph cannot pass through the origin, hence u≠0, the slope of the s-t graph is not zero. 

2. Velocity keeps decreasing from positive to zero. 

3. The slope of the v-t graph gives instantaneous acceleration, which is negative and decreasing. 

4. The slope of the s-t graph gives instantaneous velocity. As instantaneous velocity is positive and constantly decreasing, the graph s-t is also positive and constantly decreasing. 

Graphs of uniformly retarded motion and then accelerated motion: 

In this case, the graphs are drawn, and the following points are noted for the use of graph 

Let us consider a ball is thrown vertically upwards 

Important points: 

1. If a =-9.8, then the motion is under gravitational force  

2. In the graphs, O is the origin. 
   v=u and slope tanϴ=u 

3. In (graph 3) A is the maximum height of the ball reached 
   v=0 and the slope tanϴ=0 

4. B in (graph 3) is returning the ball to the ground 
   v=-u and the slope tanϴ=-u