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General SciencePhysics: Motion

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A body starts from rest and moves with a uniform acceleration of 4 m/s². What will be its velocity after 6 seconds?

12 m/s

16 m/s

20 m/s

24 m/s

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Motion

Option D

24 m/s

Quick Summary:

The correct answer is Option D (24 m/s) because the final velocity of a body starting from rest under uniform acceleration can be calculated using the first equation of motion. Given an initial velocity of $0 \text{ m/s}$ , an acceleration of $4 \text{ m/s}^2$ , and a time of $6 \text{ s}$ , the final velocity is $24 \text{ m/s}$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of pressing the gas pedal firmly in a car from a complete stop at a traffic light; if the car consistently gains speed every second, you can easily figure out how fast you are traveling after a few seconds.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'SUVAT' for kinematic variables: $s$ (displacement), $u$ (initial velocity), $v$ (final velocity), $a$ (acceleration), $t$ (time).

🔢 Key Formulas

$v = u + a \times t$ — First equation of motion relating final velocity, initial velocity, acceleration, and time

$s = u \times t + \frac{1}{2} a t^2$ — Second equation of motion for displacement

⚙️ Working Principle

According to the first equation of kinematics, final velocity ( $v$ ) equals initial velocity ( $u$ ) plus the product of acceleration ( $a$ ) and time ( $t$ ), expressed as $v = u + a \times t$ . Since the body starts from rest, the initial velocity $u = 0$ , simplifying the relation to $v = a \times t$ . Multiplying the uniform acceleration of $4 \text{ m/s}^2$ by the time interval of $6 \text{ s}$ yields the final velocity.

📌 Key Points

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Starting from rest means the initial velocity ( $u$ ) is always $0 \text{ m/s}$ .
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Uniform acceleration implies the rate of change of velocity is constant with respect to time.
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SI unit of velocity is $\text{m/s}$ and acceleration is $\text{m/s}^2$ .

✅ Advantages

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Kinematic equations allow direct calculation of motion parameters without complex calculus for uniform acceleration.

❌ Disadvantages / Limitations

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These equations are only applicable when acceleration is completely uniform or constant.

🛠️ Applications / Uses

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Calculating vehicle performance and stopping distances in transportation engineering.
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Determining trajectory and motion parameters in physics problems for competitive exams like RRB JE.

📄 Additional Information

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Constant acceleration is a foundational concept in classical mechanics.
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Option A ( $12 \text{ m/s}$ ) is incorrect because it represents the product of acceleration and half the time ( $4 \times 3$ ). Option B ( $16 \text{ m/s}$ ) would result from an acceleration of $4 \text{ m/s}^2$ for $4 \text{ seconds}$ . Option C ( $20 \text{ m/s}$ ) corresponds to $5 \text{ seconds}$ of travel.

📊 Diagram / Illustration

✅

D is correct — The final velocity calculated using the kinematic formula $v = u + at$ with $u = 0$ , $a = 4 \text{ m/s}^2$ , and $t = 6 \text{ s}$ results in $24 \text{ m/s}$ .

Core Concepts Used

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Kinematics Uniform Acceleration Equations of Motion

💡 EXAM TIP

Always verify whether the body starts from rest ( $u = 0$ ) or has an initial velocity to avoid substitution errors in exam problems.

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