Application of calculus in kinematics

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A body is bound to move along a straight line, say X-axis.It is initially at rest at origin.It moves to point (1m,0) in one second and comes to rest. How can we prove that absolute value of acceleration of this particle exceeds 4ms*2 atleast once?

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Hint:

  • Consider a scenario in which the body moves as quickly as possible given the acceleration threshold.
  • Does the body reach its goal within the given time?
  • Can any body with less acceleration be faster?