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Concept:
- Velocity: The rate of change of displacement of an object is velocity.
- Acceleration: The rate of change of velocity of an object is an acceleration.
- Equations of motion describe the behaviour of a physical system in terms of its motion as a function of time.
If an object is moving with constant acceleration 'a', initial velocity 'u', the distance travelled in tth second is given by:
\(s = u + {1\over 2}a (2t-1)\)
s is the distance travelled in tth second.
Calculation:
Given: Initial velocity of the body u = 0.
The motion under gravity so, the body is falling freely: a = g.
Distance covered in tth second:
\(s = u + {1\over 2}g (2t-1)\)
\(s = 0 + {1\over 2}g (2t-1)\)
⇒ \(s_{th} = {1\over 2}g (2t-1)\)
Distance travelled in the 1st second: t = 1;
\(s_{1} = {1\over 2}g (2\times1-1)\)
⇒ \(s_{1} = {g\over 2}\)
Distance travelled in the 2nd second: t = 2;
\(s_{2} = {1\over 2}g (2\times2-1)\)
⇒ \(s_{2} = {3\,g\over 2}\)
Distance travelled in the 3rd second: t = 3;
\(s_{3} = {1\over 2}g (2\times3-1)\)
⇒ \(s_{3} = {5\,g\over 2}\)
So, s1 : s2 : s3 = 1 : 3 : 5
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