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A block is thrown with a velocity of \( 2 m / s \) (relative to ground) on a belt, which is moving with velocity \( 4 m / s \) in opposite direction of the initial velocity of block. If the block stops slipping on the belt after \( 4 s \) of the throwing then choose the correct statement(s) This question has multiple correct options

1. Displacement with respect to ground is zero after 2.66 and displacement with respect to ground is \( 12 \mathrm{m} \) after \( 4 s \)
2. Displacement with respect to ground in \( 4 s \) is \( 4 m \).
3. Displacement with respect to belt in \( 4 s \) is \( -12 m \).
4. Displacement with respect to ground is zero in \( \frac{8}{3} s \)

Correct answer: Displacement with respect to ground is zero after 2.66 and displacement with respect to ground is \( 12 \mathrm{m} \) after \( 4 s \)

Solution

The block starts at 2 m/s while the belt moves oppositely at 4 m/s, so the block must change velocity by 6 m/s in 4 s, giving constant acceleration. Using that motion, the block’s ground displacement becomes zero at about 2.66 s and equals 12 m after 4 s, matching the given correct statement.

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