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# Graphs of Motion- Types of Motion Graphs

## 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
1. If the graph is passing through the origin, then x=0 and also y=0. Suppose no graph is passing through the origin.
1. Differentiating y with respect to x can give the slope of the graph at that point.
1. To find out the area covered in the graph, integrate y along the x-axis.
1. 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.
1. As v is constant, then the slope of the curve is constant.
1. As a=0, then the slope of the curve is zero.
1. S=vt graph starts from the origin.
1. 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.
1. s-t is a parabola as all the s-t equations are quadratic in the graph.
1. 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.
1. 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.
1. Velocity keeps decreasing from positive to zero.
1. The slope of the v-t graph gives instantaneous acceleration, which is negative and decreasing.
1. 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
1. In the graphs, O is the origin.
v=u and slope tanϴ=u
1. In (graph 3) A is the maximum height of the ball reached
v=0 and the slope tanϴ=0
1. B in (graph 3) is returning the ball to the ground
v=-u and the slope tanϴ=-u

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