A particle of mass m moves on the axis as follows : it starts from rest at t = 0 from the point x =

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A particle of mass m moves on the axis as follows : it starts from rest at t = 0 from the point x = 0, and comes to rest at t = 1 at the point x = 1. No other information is available about its motion at intermediate times (0

Accepted Answer

Since, the body is at rest at x = 0 and x = 1, α cannot be positive for all in the time interval 0 ≤ t ≤ 1.
Therefore, first the particle is accelerated and then retarded.
Now, total time t = 1 s (given)
total displacement s = 1 m (given)
s = Area under v-t graph
∴ Height or v_max =

= 2m/s is also fixed.
[Area or s =

× t × v_max]
If the height and base are fixed, area is also fixed
In case 2 : Acceleration = Retardation = 4 m/s²
In case : 1 Acceleration > 4 m/s² while
Retardation < 4 m/s²
While in case : 3 Acceleration < 4 m/s² and
Retardation > 4 m/s²
Hence, |α| ≥ 4 at some point or points in its path.

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