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Find acceleration of a bike, if starting from rest it covers a distance of x in t time.
1. \( {x\over t^2}\)
2. \( {x\over 2t^2}\)
3. \( {2x\over t^2}\)
4. \( {x\over 2t}\)

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Correct Answer - Option 3 : \( {2x\over t^2}\)

CONCEPT:

  • When a body moves in a straight line under constant acceleration, it follows three equations of motion.
  • All unknowns are found by these equations.
  1. v = u + at;
  2. s = ut + (1/2) at2 
  3. v2 = u2 + 2as

where u is initial velocity, v is final velocity, a is a constant acceleration, t is time and s is displacement.

EXPLANATION:

Given that bike starts from rest, so initial velocity u = 0; s = x and t = t

using 2nd equation of motion

s = ut + (1/2) at2 

x = 0 + (1/2) at2 ​

\(a= {2x\over t^2}\)

So the correct answer is option 3.

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