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## a body starts from rest and moving under uniform acceleration of 4 metre per second square travel half of its total path during last second

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## Answers ( )

Answer:t = 3.414 s

s = 23.3 m

Explanation:Let t be the total time of motion

Let s be the total distance of motion

s – s/2 = ½at² – ½a(t – 1²) = ½a(t² – (t – 1)²)

s/2 = ½a(t² – (t² – 2t + 1)) = ½a(t² – t² + 2t – 1)

s = a(2t – 1)

s = 4(2t – 1)

s = 8t – 4

8t – 4 = ½4t²

8t – 4 = 2t²

0 = 2t² – 8t + 4

0 = t² – 4t + 2

t = (4 ±√(4² – 4(1)(2))) / 2 = (4 ± √8)/2 = 2 ± √2

t = 3.414 s

or

t = 0.5857… s which we ignore because it does not have a full last second.

s = ½(4)3.414² = 23.3137… 23.3 m