An athlete starts running with a speed ½. Subsequently, his speed decreases by an amount that is proportional to the distance that he has already covered. The distance covered will be
Options:
(A) Linear in time
(B) Quadratic in time
(C) Exponential in time
(D) Logarithmic in time
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.36)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (2 Mark, MCQ)
- **Topic**: Linear Algebra (Systems of Linear Equations)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> An athlete starts running with a speed ½. Subsequently, his speed decreases by an amount that is proportional to the distance that he has already covered. The distance covered will be
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Systems of Linear Equations) under *Engineering Mathematics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Linear in time"*: ❌ **INCORRECT**.
- **(B)** *"Quadratic in time"*: ❌ **INCORRECT**.
- **(C)** *"Exponential in time"*: ✅ **CORRECT**.
- **(D)** *"Logarithmic in time"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.