Question

A body moving from rest with uniform acceleration travels a distance x in first ‘ t’

seconds & travels a distance y with same acceleration in next ‘2t’ seconds then which relation

is correct:

A. y= ½ X B. y= 2X C. y= 3x D. y= 4x​

Answer 1

Answer:

Correct relationship is Y = 3X

[Option.B]

Explanation:

We have :

→ Initial velocity (u) = 0

→ Distance in first 't' seconds = X

→ Distance in next '2t' seconds = Y

→ Acceleration is same.

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1st case :

By the 2nd equation of motion :

s = ut + ½at²

⇒ X = 0(t) + ½ × a × t²

⇒ X = ½at²

⇒ X = 0.5at² ----------•(1)

2nd case :

Distance travelled by the body in next '2t' seconds will be :

⇒ Y = [0(t) + ½ × a × (2t)²] - 0.5t²

⇒ Y = [½ × a × 4t²] - 0.5at²

⇒ Y = 2at² - 0.5at²

⇒ Y = 1.5at² ----------•(2)

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On dividing eq.2 by eq.1 we get :

⇒ Y/X = 1.5at²/0.5at²

⇒ Y/X = 3

⇒ Y = 3X