Acceleration Velocity Displacement vs Time Graphs

❓ Question

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive x-axis.

Identify the figures that correctly represent the motion qualitatively.

($a$ = acceleration, $v$ = velocity, $s$ = displacement, $t$ = time)

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🖼 Question Image

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✍️ Short Explanation

This problem is based on:

👉 Uniform acceleration motion
👉 Graph interpretation
👉 Relation between $a$, $v$, $s$ and $t$.

Main idea:

For constant acceleration:

$$a=\text{constant}$$
$$v\propto t$$
$$s\propto t^2$$

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🔷 Step 1 — Understand Uniform Acceleration 💯

Given:

Particle starts from rest.

So:

$$u=0$$

Acceleration is constant and positive.

Therefore:

$$a=\text{constant}$$

So acceleration-time graph must be horizontal line above time axis.

Hence graph:

$$(A)$$

is correct.

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🔷 Step 2 — Velocity-Time Relation

Using equation:

$$v=u+at$$

Since:

$$u=0$$

we get:

$$v=at$$

So velocity increases linearly with time.

Hence graph:

$$(B)$$

is correct.

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🔷 Step 3 — Displacement-Time Relation

Using:

$$s=ut+\frac12 at^2$$

Since:

$$u=0$$
$$s=\frac12 at^2$$

This is a parabola opening upward.

So slope increases continuously.

Hence graph:

$$(D)$$

is correct.

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🔷 Step 4 — Check Incorrect Graph

Graph:

$$(C)$$

shows displacement increasing linearly with time.

That represents constant velocity, not uniformly accelerated motion.

So:

$$(C)\text{ is incorrect}$$

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🔷 Step 5 — Correct Option

Correct graphs:

$$(A), (B), (D)$$

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🔷 Step 6 — JEE Trap Alert 🚨

❌ $s-t$ graph ko straight line assume kar lena

❌ Constant acceleration aur constant velocity confuse kar lena

❌ Velocity graph ka intercept ignore kar dena

Remember:

$$\boxed{ s\propto t^2 }$$

for uniform acceleration from rest.

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✅ Final Answer

$$\boxed{(A), (B), (D)}$$

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📚 Related Topics

• Acceleration Dependence on Position from Equation
• Train Crossing Time Ratio Same and Opposite Direction
• Find Time When Velocity Returns Using Acceleration Graph