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dbc

tell me something about graphical representation of motion(acceleration time graph and velocity time graph)

by v.agam

9 class.

dbc

answer??????????????????????????

titun

If the displacement of a particle, x be a function of time t,

i.e. x = f (t), then, the velocity of the paricle, v = dx/dt = f ' (t)

& acceleration of the particle, a = dv/dt = d²x/dt² = f '' (t)

In the graphical representation of motion of a particle, the following points must be remembered :

1. In the displacement-time graph, the slope of the graph at any point gives the velocity of the particle at that instant of time.

2. In the velocity-time graph, the slope of the graph at any point gives the acceleration of the particle at that intant of time.

3. In the velocity-time graph, the area under the curve gives the total displacement of the particle in the given time interval, since

_[b]

^[a] v dt = x ,where, x is the displacement of the particle in the time interval

(a-b)

Now some common questions which you will come across.

1. When x-t graph is a straight line ( x-t graph can never be perpendicular to the time axis, as it means that the particle is at diff. positions at the same instant of time which is absurd ), then v = dx/dt is constant i.e v-t graph is a st. line parallel to the time axis, and a = dv/dt = 0

2. When x-t graph is a parabola of the form x=kt², then v = 2kt i.e v-t graph is a straight line , not parallel to time axis, & a = 2k, i.e a-t graph is a st. line parallel to the time axis

3. When the v-t graph is a parabola of the form v = mt², then a=2mt, & a-t graph is a straight line passing through the origin.

Since you are in class 9, I believe, you don't know 'slope'.

'Slope' at a point means the tan ( of the angle that the tangent to the curve at that point makes with the positive X-axis )

I think you may not know about integrals much, in calculating area, mainly simple areas, formulas should be used. Like in case of a

square : area = l²sq. units , l = length of each side

rectangle : area = lb sq. units l = length b = breadth

triangle : area = 1/2 h b sq. units h = altitude b = base

parallelogram : area = b h sq. units b = base , h = height

Well, the above are the basics of graphical representation of motion of a particle. I've shown how to go about this type of problems, so hope I am of some help to you.

Cheers !!!

neeraj_agarwal_1990

well...can anybody from class 9 understand these concepts!!

avinash.sharma

The Meaning of Shape for a p-t Graph

The study of 1-dimensional kinematics has been concerned with the multiple means by which the motion of objects can be represented. Such means include the use of words, the use of diagrams, the use of numbers, the use of equations, and the use of graphs. In this article I will focuse on the use of position vs. time graphs to describe motion. The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph.

To begin, consider a car moving with a constant, rightward (+) velocity of 10 m/s. (Figure0)

If the position-time data for such a car were graphed, the resulting graph would look like the graph at the right. Note that a motion with constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph (Figure1).

Now consider a car moving with a changing, rightward (+) velocity ? that is, a car that is moving rightward and speeding up or accelerating (Figure2).

If the position-time data for such a car were graphed, the resulting graph would look like the graph at the right. Note that a motion with changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph (Figure3).

The position vs. time graphs for the two types of motion ? constant velocity and changing velocity (acceleration) ? are depicted in the Figure4

The Principle of Slope for a p?t Graph

The shapes of the position vs. time graphs for these two basic types of motion ? constant velocity motion and changing velocity motion (i.e.accelerated motion) ? reveal an important principle.

The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. It's often said, "As the slope goes, so goes the velocity."

Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right). This principle can be extended to any motion conceivable.

To explain the topic I need more pics but limit is only 5 pics at a time. So Please ask about acceleration graph as a new question.

edison

Thats perfect answer.

devesh_l2k007

and 1 more thing take care that the parabola oens up when acc and down wen dec

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The Meaning of Shape for a p-t Graph

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