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Answers
Suppose a body is moving with initial velocity “Vi” after time t its velocity becomes Vf. The distance covered by the body is “S”.The acceleration of the body is represented by a.
Consider the speed-time graph in which the initial velocity “Vi” of the body is represented by “OA”.After a time interval, OC the speed of the body changes uniformly and becomes “Vf” which is represented by line BC in the graph.
Consider the speed-time graph in which the initial velocity “Vi” of the body is represented by “OA”.After a time interval, OC the speed of the body changes uniformly and becomes “Vf” which is represented by line BC in the graph.The slope of the graph is AB which is the acceleration “a”.
The distance travelled by the speed time graph is calculated as:
Mathematical proof:
It is clear from the given figure that:
S=Area of OABC
S=ar(OADC)+ar(ABD)
S={l×b}+{1/2(b×h)}
S={OA×OC}+{1/2(AD×BD)}
S=(u×t)+(1/2×t×at)
S=ut+1/2at^2
second equation of motion derivation
second equation of motion derivationThis is the second equation of motion, which shows the relationship of distance, initial velocity, time and acceleration.
∫σr αccurατξ α∩δωεrδ :
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