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प्रश्न
Derive the equation
S = ut+ `1/2` at2
Using a speed- time graph
उत्तर
The area enclosed under a velocity time curve gives the distance covered by a moving body. So total distance S covered by a uniformly accelerating body is given by area of trapezium OSQP.
S = area of trapezium OSQP.
AREA of rectangle OSRP + area of triangle PRQ.
S = OP x OS + `1/2` PR xQR.
s = u x t + `1/2` x t x at
S = ut + `1/2` at2
This is known as second equation of motion.
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