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.
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.
OA = ED = u
OC = EB = v and
OE = t = AD.
1. Equation for velocity-time relation.
Acceleration is given by slope of velocity-time graph AB
Acceleration is given by slope of velocity-time graph AB
Hence, the first equation of motion is proved.
2. Equation for position-time relation:
From the first part, we have
From the first part, we have
This proves the second equation of motion.
3. Equation for position-velocity relation:The distance travelled by object in time t is,
s = Area of trapezium OABE
Acceleration, a = slope of velocity-time graph AB.
s = Area of trapezium OABE
Acceleration, a = slope of velocity-time graph AB.
Hence, the third equation of motion is also proved.
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