NDA (I) 2025 General Ability Test · Question 145 of 150

Correct — C, u² − v² = 2as. The genuine third equation of motion is v² − u² = 2as, which rearranges to u² − v² = −2as. Option (c) drops the minus sign and writes u² − v² = 2as, so it is the incorrect equation. The other three are all standard results for uniformly accelerated motion.

• (a)s = ut + ½ at² — This is the correct second equation of motion, giving displacement in time t; it is valid.
• (b)u = v − at — This is just the first equation v = u + at rearranged, so it is correct, not the odd one out.
• (d)Distance travelled during nᵗʰ second = u + ½ a(2n − 1) — This is the correct formula for the distance covered in the nth second, sₙ = u + (a/2)(2n − 1); it is valid.

For motion with constant acceleration the three equations of motion are v = u + at, s = ut + ½at², and v² = u² + 2as, plus the distance-in-nth-second result sₙ = u + (a/2)(2n − 1). Here u is initial velocity, v final velocity, a acceleration, s displacement and t time. Getting a sign or a rearrangement wrong is the classic error the question exploits.

Each option is a valid kinematic relation except one, where a sign has been flipped. Recall the true form v² − u² = 2as and compare: option (c) writes u² − v² = 2as, missing the negative sign, so it is the incorrect statement.

• The first equation of motion, v = u + at, rearranges to u = v − at.
• The second equation of motion, s = ut + ½at², gives displacement in time t.
• The third equation of motion is v² − u² = 2as, i.e. u² − v² = −2as, not +2as.
• The distance covered in the nth second is sₙ = u + (a/2)(2n − 1).

• Overlooking a flipped sign — v² − u² = 2as, not u² − v² = 2as.
• Assuming a rearranged equation (u = v − at) is wrong when it is just the first equation restated.

Asked by listing kinematic equations and asking which is incorrect, or by using an equation of motion in a numerical problem.

No directly related past PYQ was found.

• practice — not a real PYQ

  The correct third equation of motion for uniform acceleration is

  • (a)v² = u² + 2as
  • (b)u² = v² + 2as
  • (c)v² = u² − 2as always
  • (d)v² − u² = as

  Answer(a) v² = u² + 2as — the standard velocity–displacement relation.

• practice — not a real PYQ

  The distance covered by a uniformly accelerated body in the nth second is given by

  • (a)u + a(2n − 1)
  • (b)u + ½ a(2n − 1)
  • (c)u + ½ an²
  • (d)un + ½ an²

  Answer(b) u + ½ a(2n − 1) — the standard distance-in-nth-second formula.