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 le t le 1`
B. `|alpha|` cannot exceed 2 at any point in its path
C. `|alpha|` be `ge` 4 at point or some points in its path
D. Both a and c are correct

Answer

D

Explanation

Since, at t = 0 and t = 1s, particle is in rest. This is possible only when the particle accelerated for sometime and then decelerates to come in rest.