## 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.

### 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 at^{2}

s = ut + 1/2 at^{2}**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

=( EB^{2} – ED^{2} ) / 2a

v^{2} – u^{2} = 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

What is wave motion ? click here

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

what is acceleration ? click here

what is speed ? click here

what is velocity ? click here