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General SciencePrevious Year Paper 2024

Select the correct equation(s) that relate(s) the final and initial velocity of a freely falling object with respect to time. (A) $s = ut + 2at^2$ (B) $v = u + \frac{1}{2}at$ (C) $(v - u) = at$

Only (A)

and (B)

and (C)

Only (C)

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option D

Only (C)

Quick Summary:

The relationship between velocity, acceleration, and time for an object under uniform acceleration is defined by the first equation of motion, $v = u + at$ . Rearranging this equation to isolate the change in velocity gives $(v - u) = at$ .

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💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

If you are driving a car and increase your speed from 20 km/h to 60 km/h over 10 seconds, the 'gain' in your velocity is directly proportional to how hard you press the accelerator (acceleration) and for how long you press it (time).

🔢 Key Formulas

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

$(v - u) = at$ — The equation relating the change in velocity to acceleration and time

⚙️ Working Principle

According to Newton's law of motion, acceleration is the rate of change of velocity: $a = \frac{v - u}{t}$ . By multiplying both sides by time $t$ , we obtain the expression $(v - u) = at$ , where $v$ is final velocity, $u$ is initial velocity, $a$ is acceleration, and $t$ is time.

📌 Key Points

▸
Acceleration is defined as the change in velocity per unit time.
▸
For a freely falling object, the acceleration $a$ is equal to the acceleration due to gravity $g$ (approx $9.8 m/s^2$ ).
▸
The equation $(v - u) = at$ is a direct derivation of the basic kinematic definition of acceleration.

✅ Advantages

▸
Allows for simple calculation of final velocity when initial velocity, acceleration, and time are known.

❌ Disadvantages / Limitations

▸
Only applicable under conditions of uniform acceleration.

🛠️ Applications / Uses

▸
Calculating impact speed of falling objects
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Analyzing motion in free-fall experiments

📄 Additional Information

▸
Option (A) is incorrect because the standard kinematic equation is $s = ut + \frac{1}{2}at^2$ .
▸
Option (B) is incorrect because the factor $\frac{1}{2}$ belongs to the displacement equation, not the velocity-time relationship.

📊 Diagram / Illustration

✅

D is correct — The equation $(v - u) = at$ correctly represents the change in velocity resulting from constant acceleration over a period of time.

Core Concepts Used

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Kinematics Equations of Motion Uniform Acceleration

💡 EXAM TIP

Always verify units when working with kinematic equations; ensure time is in seconds and acceleration is in $m/s^2$ to get velocity in $m/s$ .

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