At uniform speed the acceleration is

Q: What is the answer to NDA (I) 2025 GAT Q150?

C. Correct — C, Zero. Acceleration is the rate of change of velocity. When a body moves at uniform speed along a straight line its velocity does not change in magnitude or direction, so the change in velocity is zero and therefore the acceleration is zero. (The one exception is motion in a curve, such as uniform circular motion, where the direction keeps changing and there is a centripetal acceleration even though the speed is constant — but for straight-line uniform speed the acceleration is zero.) (Provisional — pending the official UPSC key.)

(a)Maximum
(b)Minimum
(c)Zero
(d)Constant

Answer

Why

Correct — C, Zero. Acceleration is the rate of change of velocity. When a body moves at uniform speed along a straight line its velocity does not change in magnitude or direction, so the change in velocity is zero and therefore the acceleration is zero. (The one exception is motion in a curve, such as uniform circular motion, where the direction keeps changing and there is a centripetal acceleration even though the speed is constant — but for straight-line uniform speed the acceleration is zero.)

Why the others are wrong

(a)
Maximum — Acceleration is largest when velocity changes most rapidly; at uniform speed the velocity is not changing at all, so it cannot be maximum.
(b)
Minimum — 'Minimum' is vague; the acceleration is not merely small but exactly zero when the speed is uniform in a straight line.
(d)
Constant — Zero is indeed a constant value, but the precise and intended answer is that the acceleration is zero, not simply some non-zero constant.

Concept

Speed is the magnitude of velocity; velocity also has direction. Acceleration is the rate of change of velocity, so a body accelerates only if its speed OR its direction changes. Moving at a steady speed in a straight line means constant velocity, hence zero acceleration. Uniform circular motion is the special case where speed is constant but direction changes, giving a non-zero (centripetal) acceleration.

The options tempt you with 'constant' (true in the trivial sense that zero is constant) and 'minimum'. The exact answer for uniform speed in a straight line is that the acceleration is zero, because the velocity is unchanging.

Key facts

Acceleration = change in velocity ÷ time; it is zero when velocity is constant.
Uniform speed in a straight line means constant velocity and hence zero acceleration.
On a velocity–time graph, uniform velocity is a horizontal line whose slope (acceleration) is zero.
In uniform circular motion the speed is constant but a centripetal acceleration exists because the direction changes.

Study next

Distinguishing speed, velocity and accelerationVelocity–time and position–time graphsUniform versus non-uniform motionUniform circular motion and centripetal accelerationEquations of motion for uniform acceleration

Common traps

Choosing 'constant' — although zero is constant, the intended answer is that acceleration is zero.
Assuming constant speed always means zero acceleration; in circular motion direction changes, so there is centripetal acceleration.

Asked directly about acceleration at uniform speed, or by reading the slope of a velocity–time graph.

Related PYQs

NDA_GAT_2024_II_Q912024Open & attempt →

A vehicle starts moving along a straight-line path from rest. In first t seconds it moves with an acceleration of 2 m/s² and then in next 10 seconds it moves with an acceleration of 5 m/s². The total distance travelled by the vehicle is 550 m. The value of time t is

(a) 10 s
(b) 13 s
(c) 20 s
(d) 25 s

Answer(a) 10 s

Same concept — the link between velocity, acceleration and motion along a straight line. That NDA item works with non-zero accelerations to find a time; this one tests the base case where uniform speed means the acceleration is zero.

Practice

practice — not a real PYQ
On a velocity–time graph, motion with zero acceleration is represented by
- (a)a straight line sloping upward
- (b)a horizontal straight line
- (c)a curve bending upward
- (d)a straight line sloping downward
Answer(b) a horizontal straight line — constant velocity means zero slope, i.e. zero acceleration.
practice — not a real PYQ
A body moving in a circle at constant speed has
- (a)zero acceleration
- (b)acceleration directed towards the centre
- (c)acceleration along its motion
- (d)decreasing speed
Answer(b) acceleration directed towards the centre — its direction changes, giving centripetal acceleration even at constant speed.