A particle of mass `m` moves on the ` x- axis ` as follows : it starts from rest at ` t = 0`, from the point `x = 0`, and comes to rest at ` t = l` at the point `x = 1`. No other information is available about its motion at intermediate times `( 0 lt t lt l)` . If `alpha ` denotes the instantaneous accelartion of the particle , then :

Options

A. `alpha` cannot remain positive for all t in the interval `0`lt`=t`lt`=1`.
B. `|alpha|` cannot exceed 2 at any point in its path.
C. `|alpha|` must be `gt`=`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

A, D

Explanation

a,d. `alpha` cannot remain positive for all t in the interval `0letle1`. This
is because since the body starts from rest, it will first accelerate,
finally it stops therefore a will become negative. Therefore,
a will change its direction. Hence, (a) and (d) are the correct
options.