a point moving along the x direction starts from rest at x=0 and comes to rest at x=1 after 1 second. its accelaration is denoted by a at any point. which of the following is incorrect?
1] a must change sign during motion
2] |a| >= 4 units at some or all points during the motion
3] it is not possible to specify upper limit for |a|
4] |a| cant be less than 1/2 during the motion.

Dear Goutham,

Statement 1 need not always true,

Since its possible that the point is retarding before x=0,

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But the answer is option 4. Can anyone please tell how?

Validity of (a)

Since the particle is starting and ending its journey at rest as specified in the question and is doing a + displacement,its obvious that it had to accelerate and deaccelerate too in the interval.

Validity of (b). 

The least acceleration the particle can have in the journey is when the particle has a constant and equal accleration and deacceleration during the entire journey. If it is not so either modulus of acceleration will greater than the least or modulus of decceleration will be greater then the least. as such the least acceleration that the particle can have is 4m/s.

Validity of (c)

As clearer the from above explantaion that there is a restriction to least value of acceleration but not the uper limit.

Ex. It can have a positive infinite acceleration for a infinitesiemally small time interval it can reach to a velocity 1m/s then move with a uniform velocity for 1s to cover the distance and deaccelerate again to get reach 0 velocity. In this way it ends and starts its journey at rest but covers a certain distance.     

Contradiction for (d)

Now if the particle can move with uniform velocity during any instant of time, definitely it will have 0 accelereation at some points. But  clearly note tht im taking about only some point. Still the modulus of acceleration or deacceleration will have to be greater that 1/2 at some points during the entire journey . 

So (d) seems to be the correct answer

How do you get tehat the least value of accelaration or decelaration is 4 units?

and could you please tell me how you arrived at the last option? 

But hats off to you....you can solve every single problem without any trouble.