Question 93 of 308

A bullet is shot vertically downwards with an initial velocity of $100m{s}^{-1}$ from a certain height. Within $10s$, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $t=20s$ will be : (Take $g=10m{s}^{-2}$)

ABCD

Show answer and solution▾

Answer: (A)

As the upward direction is taken as positive, the velocity at $t=0$ is $u=-100m{s}^{-1}$.
As it is falling under gravity, its acceleration is constant and $a=-10m{s}^{-2}$.
Applying equation of motion for constant acceleration during the time of fall i.e., for $0$ to $10s$,
$v=u+at \Rightarrow v=-100-10\times 10 \Rightarrow v=-200m{s}^{-1}$
After $10s$ it hits the ground and remains at rest.
Therefore, option A is the correct representation.