Question
Derive the equation
$S=u t+\frac{1}{2} a^2$
Using a speed- time graph
$S=u t+\frac{1}{2} a^2$
Using a speed- time graph
✓
Answer
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.
$S=\text { area of trapezium OSQP. }$
AREA of rectangle OSRP + area of triangle PRQ.
$ S=O P \times O S+\frac{1}{2} P R \times Q R$
$S=u \times t+\frac{1}{2} \times t \times \text { at }$
$S=u t+\frac{1}{2} at ^2 $
This is known as second equation of motion.
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