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 $-2m/s^2$. Then

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

Answer 1

Answer: (B), (C)

The correct options are
B Its initial speed is 8 m/s.
C Distance travelled in 9 sec is 41 m.

By $v^2-u^2=2as,$
$(-10{)}^2-u^2=2\times -2\times -9\Rightarrow u=8m/s$
$\therefore$ Initial speed is $8m/s$
The time after which it reaches origin say is $t$,
By $S=ut+\frac{1}{2}a{t}^2$
$0=10t-\frac{1}{2}\times 2t^2$
$t^2-10t=0\Rightarrow t=0sec$ or $t=10sec$

When it reaches the extreme position on the right, say it has covered at $d$ then,
$0^2-8^2=2\times -2\times d\Rightarrow d=16m$
The total distance covered is,
$(2\times 16)+9=41m$