Question

A body accelerates from rest and travels 'S¹' in 't' seconds . It travels uniformly with acquired velocity for next 't' seconds and covers 'S²'.Then

Options:
S¹=S²
S¹=2S²
S²=2S¹
S²=4S¹

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Answer 1

Given :

A body accelerates from rest and travels S₁ in t seconds.

After that it travels uniformly with acquired velocity for next t second and covers S₂.

To Find :

Relation between S₁ and S₂.

Solution :

■ During first t seconds, body is moving with constant acceleration means velocity will vary with time.

Let acceleration of body be a.

Initial velocity of body is zero.

Let's apply second equation of kinematics.

➙ S₁ = ut + 1/2 at²

➙ S₁ = (0 × t) + 1/2 at²

➙ S₁ = 1/2 at² ..... (i)

Final velocity of body after time t :

➝ v = u + at

➝ v = 0 + at

➝ v = at

Final velocity of first case will be initial velocity of second case. In this case body is moving with a constant velocity$.$

⇒ velocity = distance / time

⇒ at = S₂ / t

⇒ S₂ = at² ..... (ii)

Taking ratio of (i) & (ii), we get

➠ S₁ / S₂ = 1/2 at² / at²

➠ S₁ / S₂ = 1 / 2

➠ S₂ = 2S₁

∴ (3) is the correct answer!

Answer 2

Answer:

hope it helps you this answer in image