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A particle of mass m moves on the x- ax...

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 :

A

` alpha ` cannot remain positive for all t in interval ` 0le t le 1`

B

`|alpha| `must be `ge` 4 at same point or points in its path

C

`|alpha| ` 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

Text Solution

Verified by Experts

The correct Answer is:
A, C
Since the body is at rest at x = 0 and x = 1. Hence` alpha` , cannot be positive for all time in the interval `0 lt t lt 1` . Therefore, first the particle is accelerated and then retarded. Now, total time t = 1s (given) Total displacement s = 1m (given) S = area under v – t graph
Height or ` v_(max) =(2s)/(t) = 2m//s ` is also fixed
[Area or ` s=(1)/(2) xx txx v _(max) ]`
In case 2 : Acceleration = Retardation = ` 4 m//s^(2) `
In case 1: Acceleration `gt 4m//s^(2) and `Retardation `lt 4 m//s^(2) `
while in case 3: Acceleration `lt 4m//s^(2) ` and Retardation Hence , `|alpha |ge 4 ` at some point or points in its path.
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