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General SciencePhysics: Motion

A vehicle traveling at 40 m/s applies brakes and comes to a complete stop in 8 seconds. What is the magnitude of its acceleration (in m/s²)?

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Motion

Option A

Quick Summary:

Acceleration is the rate of change of velocity over time. Since the vehicle comes to a stop, the final velocity is $0 \text{ m/s}$ , and the magnitude of acceleration is calculated by the change in velocity divided by the time interval.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of this as the 'braking intensity' needed to halt your car; the harder you press the brakes, the shorter the time it takes to stop, resulting in a higher magnitude of deceleration.

🧠 Memory Mnemonic / Shortcut Aid

VAT: $v = u + at$ (Velocity, Acceleration, Time relation).

🔢 Key Formulas

$a = \frac{v - u}{t}$ — Definition of acceleration

$v = u + at$ — First equation of motion

⚙️ Working Principle

According to Newton's first law and the kinematic definition of acceleration, $a = \frac{v - u}{t}$ . Given the initial velocity $u = 40 \text{ m/s}$ and final velocity $v = 0 \text{ m/s}$ , the change in velocity is $-40 \text{ m/s}$ . Dividing this by the time $t = 8 \text{ s}$ yields an acceleration of $-5 \text{ m/s}^2$ . The magnitude is the absolute value, which is $5 \text{ m/s}^2$ .

📌 Key Points

▸
Acceleration is a vector quantity, while speed/magnitude is scalar.
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Deceleration (or retardation) occurs when the acceleration vector points in the opposite direction of velocity.
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Final velocity is $0 \text{ m/s}$ when a body comes to rest.

🛠️ Applications / Uses

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Automotive braking system analysis
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Safety testing for crash performance

📄 Additional Information

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SI unit of acceleration is $\text{m/s}^2$ .
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Option B (8) is obtained if one incorrectly calculates $40/5$ or confuses variables.
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Option C (4) results from $40/10$ or algebraic errors.
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Option D (10) results from $40/4$ .

📊 Diagram / Illustration

✅

A is correct — The magnitude of acceleration is calculated as $\frac{|0 - 40|}{8} = 5 \text{ m/s}^2$ .

Core Concepts Used

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Kinematics Uniform acceleration Negative acceleration

💡 EXAM TIP

Always identify the direction of acceleration. If speed is decreasing, the sign of $a$ must be opposite to the sign of $u$ .

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