Question

A particle moves along $x$-axis as follows: It starts from rest at $t=0$ from a point $x=0$ and comes to rest at $t=1$ at a point $x=1$. No other information is available about its motion for the intermediate time $0<t<1$. If $\alpha$ denotes the instantaneous acceleration of the particle, then

• A. $\alpha$ cannot remain positive for all $t$ in the interval $0\le t\le 1$
• B. $\left|\alpha \right|$ cannot exceed 2 at any point in its path
• C. $\left|\alpha \right|$ must be $\ge 4$ at some point or points in its path
• D. $\alpha$ must change sign during the motion, but no other assertion can be made with the information given

Answer 1

The correct option is A $\alpha$ cannot remain positive for all $t$ in the interval $0\le t\le 1$

Correct options: A and D

Explanation: Here, cannot remain positive for all the time. Because at first the particle was at rest at t=0 in the position x=0, so its acceleration was 0. Then it started to move and stopped at the position x=1. It must have to accelerate first and then decelerate to come rest at t=1 in the position x=1.

From the above explanation it is clear that cannot remain positive for all t in the interval . Again for the middle period there is no information given. But, during this time there may be acceleration or deceleration. So, no other assertion can be made with the given information.