NDA (I) 2025 GAT Q130: A car has an initial velocity of 12 m/s and is brought to

Q: What is the answer to NDA (I) 2025 GAT Q130?

C. Correct — C, -1.6 m/s^2. Using v^2 = u^2 + 2as with u = 12 m/s, v = 0 and s = 45 m: 0 = 12^2 + 2a(45), so 0 = 144 + 90a and a = -144/90 = -1.6 m/s^2. The negative sign shows retardation — the car is slowing down. (Provisional — pending the official UPSC key.)

NDA (I) 2025 General Ability Test · Question 130 of 150

Question text verified against the official NDA question paper.

Provisional answers. UPSC has not yet released the official NDA 2025 answer key (it is published several months after the exam). The answers here are our best-supported answers — derived from careful subject-solving and cross-checked against independent solved papers and primary sources — and will be reconciled to the official key as soon as UPSC publishes it. They are not the official UPSC answer key.

A car has an initial velocity of 12 m/s and is brought to rest over a distance of 45 m. The acceleration of the car is

(a)+1.6 m/s²
(b)+3.2 m/s²
(c)−1.6 m/s²
(d)−0.8 m/s²

Answer

Why

Correct — C, -1.6 m/s^2. Using v^2 = u^2 + 2as with u = 12 m/s, v = 0 and s = 45 m: 0 = 12^2 + 2a(45), so 0 = 144 + 90a and a = -144/90 = -1.6 m/s^2. The negative sign shows retardation — the car is slowing down.

Why the others are wrong

(a)+1.6 m/s^2 — Right magnitude but wrong sign — a decelerating car has a negative acceleration, not a positive one.
(b)+3.2 m/s^2 — This uses 144/45 (dropping the factor of 2 in 2as) and also has the wrong sign.
(d)-0.8 m/s^2 — This halves the correct value by dividing 144 by 180 instead of 90.

Concept

For motion with uniform acceleration, the equation v^2 = u^2 + 2as links the final velocity v, initial velocity u, acceleration a and displacement s without needing time. When a body is brought to rest, v = 0, and solving gives a negative a — a retardation.

Choose the kinematic equation that omits time, since only u, v and s are given. Be careful with the factor of 2 (it is 2as, not as) and with the sign: 'brought to rest' means v = 0 and a comes out negative.

Key facts

v^2 = u^2 + 2as is the time-independent equation of motion.
With u = 12 m/s, v = 0 and s = 45 m, a = -144/90 = -1.6 m/s^2.
A negative acceleration (retardation) means the car is decelerating.
The magnitude is 1.6 m/s^2; the minus sign only shows the direction opposite to motion.

Deceleration from v^2 = u^2 + 2as

v^2 = u^2 + 2as→u = 12 m/s, v = 0, s = 45 m

0 = 144 + 90a→solve for a

a = -144 / 90→a = -1.6 m/s^2 (retardation)

The negative result shows the car is decelerating — option (c).

Study next

The three equations of uniformly accelerated motionDifference between speed, velocity and accelerationSign convention for retardation and decelerationStopping distance and brakingDistance-time and velocity-time graphs

Common traps

Include the factor of 2 in 2as; do not divide 144 by 45.
'Brought to rest' fixes v = 0 and yields a negative (retarding) acceleration.

Numerical kinematics: given u, v and s (or t), find the acceleration or distance using the equations of motion.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
A body moving at 20 m/s is brought to rest in 100 m. Its retardation is
- (a)1 m/s^2
- (b)2 m/s^2
- (c)4 m/s^2
- (d)5 m/s^2
Answer(b) 2 m/s^2 — a = -(20^2)/(2 x 100) = -2 m/s^2.
practice — not a real PYQ
Which equation of motion does not contain time?
- (a)v = u + at
- (b)s = ut + (1/2)at^2
- (c)v^2 = u^2 + 2as
- (d)s = vt
Answer(c) v^2 = u^2 + 2as — it relates velocity and displacement without time.