Question

A body starts from rest and travels with uniform acceleration. If the distance covered in first \(2\) seconds is \(x\) and next \(2\) seconds is \(y\), then

• A. \(y=x\)
• B. \(y=2x\)
• C. \(y=3x\)
• D. \(y=4x\)

Hint:

For uniformly accelerated motion from rest, distances in successive equal time intervals are in the ratio \(1:3:5:\cdots\).

Answer 1

The Correct Option is C

Concept:
For a body starting from rest with uniform acceleration: \[ s=\frac{1}{2}at^2 \]

Step 1: Distance covered in first \(2\) seconds: \[ x=\frac{1}{2}a(2)^2 \] \[ x=2a \]

Step 2: Distance covered in first \(4\) seconds: \[ s_4=\frac{1}{2}a(4)^2 \] \[ s_4=8a \]

Step 3: Distance covered in next \(2\) seconds: \[ y=s_4-x \] \[ y=8a-2a \] \[ y=6a \]

Step 4: Since \(x=2a\): \[ y=3x \] \[ \boxed{y=3x} \]