Question

A street car moves rectilinearly from station (here car stops) to the next station (here also car stops) with an acceleration varying according to the law , where and are positive constants and is the distance from station A. The distance between the two stations & the maximum velocity are:

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Given that acceleration of car is

For maximum velocity, acceleration should be zero.


At , the particle has its maximum velocity.
We use

At

Substituting gives maximum velocity as

Also, the velocity of the car should become zero at station .


Distance between the stations is .
Alternate : means particle will execute SHM.
At mean position;

In the figure shown, is the mean position and are extreme positions