Motion In A Straight Line

Physics
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A particle moves with a non zero initial velocity and retardation , where is the velocity at any time .

A
The particle will cover a total distance
B
The particle comes to rest at
C
Particle continues to move for long time
D
at time
Hard
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STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

STATEMENT-2: 
If the observer and the object are moving at velocities and respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is .

A
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C
STATEMENT -1 is True, STATEMENT-2 is False
D
STATEMENT -1 is False, STATEMENT-2 is True
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A ball is thrown vertically upwards (relative to the train) in a compartment of a moving train. The face of the person sitting inside the compartment is towards engine of the train.

A
The ball will maintain the same horizontal velocity as that of the person (or the compartment) at the time of throwing.
B
If the train is accelerating then the horizontal velocity of the ball will be different from that of the train velocity, at the time of throwing.
C
If the ball appears to be moving backward to the person sitting in the compartment it means that speed of the train is increasing.
D
If the ball appears to be moving ahead of the person sitting in the compartment it means the train's motion is retarding.
Hard
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A circus girl throws three rings upwards one after the other at equal intervals of half a second. She catches the first ring half second after the third was thrown. Then,
( acceleration due to gravity)

A
the velocity of projection of rings is
B
the maximum height attained by rings is
C
when the first ring returns to her hand, the second ring was coming downwards and it is on the height of (from the ground).
D
when the first ring returns to her hand, the third ring was going up and has travelled a distance of (from the ground).
Hard
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