equation of motion by graphical method free

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equation of motion by graphical method free formula

equation of motion by graphical method formula or Derive the equations of motion for uniformly accelerated motion from velocity-time graph.
Ans- Equations of motion by graphical method. Consider an object moving along a straight line with initial velocity u and uniform acceleration a. Suppose, it travels distance s in time t. As shown in Fig. 8.19, its velocity-time graph is straight line. Here OA = ED = u,
OC = EB = v and OE = t = AD.

equation of motion by graphical method
equation of motion by graphical method

1-First equation of motion

1-Equation for velocity-time relation. We know that
Acceleration = Slope of velocity-time graph AB

 \displaystyle \begin{array}{l}a=\frac{{DB}}{{AD}}=\frac{{DB}}{{OB}}\\\\a=\frac{{EB-ED}}{{OE}}\\\\a=\frac{{v-u}}{t}\end{array}

v-u = at
v = u + at
This proves the first equation of motion.

2-Second equation of motion

Equation for position-time relation.
From the above part, we have
a = DB / AD
= DB / t
DB = at
Distance travelled by the object in time t is
s = Area of the trapezium OABE
= Area of rectangle OADE + Area of triangle ADB
= OA x OE + 1/2 DB x AD
= ut + 1/2 at2
s = ut + 1/2 at2
This proves the second equation of motion.

3-Third equation of motion

Equation for position-velocity relation. The distance travelled by object in time t is
s = Area of trapezium OABE
=1/2 ( EB + OA ) x OE
= 1/2 ( EB + ED) x OE
Acceleration, a = Slope of velocity-time graph AB
a = DB / AD
= DB / OB
= ( EB – ED ) / OE
OE=(EB – ED ) / a
=1/2 (EB + ED ) x (EB – ED) / a
=( EB2 – ED2 ) / 2a
v2 – u2 = 2as
This proves the third equation of motion

What is the nature of the distance-time graphs for uniform and non-uniform motion of an object ?
Ans- For uniform motion, the distance-time graph is a straight line inclined with the time-axis. For non-uniform motion, the distance-time graph is a curve.

What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis ?
Ans-The object is at rest.

What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis ?
Ans- The object has a uniform speed.

What is the quantity which is measured by the area occupied below velocity-time graph ?
Ans- Distance covered by the body in the given time interval.

Importent Question….

What is motion ? click here
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What is Periodic Motion ? click here
What is Time Period ? click here
What is Displacement ? click here
What is vibration ? click here
What is Oscillatory Motion ? click here
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