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Question

A particle is moving along the x-axis such that at t = 0, it is at origin, and when it is at x=9m, its velocity is v=10m/s. Its acceleration is uniform and is equal to 2m/s2. Then

A
Time after which it reached origin is 9 sec.
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B
Its initial speed is 8 m/s.
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C
Distance travelled in 9 sec is 41 m.
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D
Distance travelled in 9 sec is 9m.
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Solution

The correct options are
B Its initial speed is 8 m/s.
C Distance travelled in 9 sec is 41 m.
By v2u2=2as,
(10)2u2=2×2×9u=8 m/s
Initial speed is 8 m/s
The time after which it reaches origin say is t,
By S=ut+12at2
0=10t12×2t2
t210t=0t=0 sec or t=10 sec

When it reaches the extreme position on the right, say it has covered at d then,
0282=2×2×dd=16 m
The total distance covered is,
(2×16)+9=41 m

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