Which graph represents uniform acceleration ? (a) graph (a) -- straight line through origin, constant slope (b) graph (b) -- triangular rise-then-fall (c) graph (c) -- concave-up increasingly steep curve (d) graph (d) -- concave-down flattening/saturating curve

> > [!TLDR] > A displacement-time graph for uniform acceleration is a concave-up curve that gets steeper with time, since s depends on t^2 -- graph (c). > > For motion with uniform (constant) acceleration a, the displacement-time relation is > s = ut + (1/2)a t^2 > > This is a quadratic function of time. Its slope, ds/dt = u + at, is the instantaneous velocity, which increases steadily with time for positive a. A steadily increasing slope means the curve bends upward more and more sharply as t increases -- this is exactly a concave-up curve that starts at the origin and curves increasingly steeply, matching graph (c). > > By contrast: > (a) a straight line through the origin with constant slope describes UNIFORM VELOCITY (zero acceleration), not uniform acceleration. …

Which graph represents uniform acceleration ? (a) graph (a) -- straight line through origin, constant slope (b

Question 60 of 89

Q. Which graph represents uniform acceleration ?

(a) graph

(a) -- straight line through origin, constant slope

(b) graph

(b) -- triangular rise-then-fall

(d) graph

(d) -- concave-down flattening/saturating curve

Tamil Nadu DgeTamil Nadu HSC First Year (DGE) Board 2019MCQ· 1mImportance★★★★★

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Concept understanding — Uniformly Accelerated Motion

Uniformly Accelerated Motion

Imagine you're sitting in a train that starts moving from a station. At first, it crawls — then it picks up speed smoothly, second by second. If you watch the speedometer, you might see it climb by the same amount every second: 0 to 10 km/h, then 10 to 20, then 20 to 30. That steady, predictable increase is the heart of uniformly accelerated motion.

The Intuition

When something moves with uniform acceleration, its velocity changes by the same amount in every equal interval of time. The change is constant — not faster one second and slower the next.

Think of a ball rolling down a gentle, straight ramp. It starts from rest. In the first second, it gains some speed. In the next second, it gains exactly the same amount of speed again. The acceleration — the rate of change of velocity — is fixed.

Note

"Uniform" here means "constant" or "unchanging." It does not mean the speed is constant. In fact, the speed is changing — but the rate at which it changes is constant.

The Precise Statement

Uniformly accelerated motion is motion in a straight line where the acceleration $a$ is constant in both magnitude and direction.

Mathematically, if $v$ is velocity at time $t$ , and $u$ is the initial velocity (at $t = 0$ ), then:

a = \frac{v - u}{t} = \text{constant}

This single idea leads to the three famous equations of motion (for constant acceleration):

v = u + at

Here:

$u$ = initial velocity (at $t = 0$ )
$v$ = velocity at time $t$
$a$ = constant acceleration
$s$ = displacement in time $t$

What It Looks Like in Real Life

Situation	Acceleration	Why it's (approximately) uniform
A car accelerating on a highway	~2–3 m/s²	Engine provides roughly constant force
A ball dropped from a height	9.8 m/s² downward	Gravity is nearly constant near Earth's surface
A train starting from a station	~0.5 m/s²	Controlled by the driver to be smooth

Watch out

Not all motion is uniformly accelerated. A car stopping suddenly has deceleration that changes — it's not uniform. A roller coaster has acceleration that varies wildly. Uniform acceleration is an ideal model that works beautifully for many real situations (like free fall) but not all.

The Key Insight

The word "uniform" refers to the acceleration, not the velocity. If acceleration is constant, then:

Velocity changes linearly with time (a straight line on a $v$ - $t$ graph)
Displacement changes quadratically with time (a parabola on an $s$ - $t$ graph)

This is why the equations above are so powerful: they let you predict position and velocity at any instant, as long as acceleration stays constant.

Important

For uniformly accelerated motion, the $v$ - $t$ graph is always a straight line. The slope of that line equals the acceleration. If the graph is curved, acceleration is not uniform. …

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Q.Which graph represents uniform acceleration ?