A car 2 m long travelling at `30 ms^(-1)` overtakes another car 4 m long travelling at `20 ms^(-1)`. The time taken by the first car to pass the second car is

Options

A. 0.2 s
B. 0.4 s
C. 0.6 s
D. 0.8 s

Answer

To solve the problem of how long it takes for the first car to overtake the second car, we can follow these steps:

### Step 1: Understand the scenario
- We have two cars:
- Car A (2 m long) traveling at 30 m/s
- Car B (4 m long) traveling at 20 m/s
- Car A is trying to overtake Car B.

### Step 2: Determine the relative speed
- Since both cars are moving in the same direction, we need to find the relative speed of Car A with respect to Car B.
- The relative speed \( v_{relative} \) is given by:
\[ v_{relative} = v_A - v_B = 30 \, \text{m/s} - 20 \, \text{m/s} = 10 \, \text{m/s} \]

### Step 3: Calculate the total distance to be covered
- To completely overtake Car B, Car A needs to cover the length of Car B plus its own length.
- The total distance \( d \) that Car A needs to cover is:
\[ d = \text{Length of Car B} + \text{Length of Car A} = 4 \, \text{m} + 2 \, \text{m} = 6 \, \text{m} \]

### Step 4: Calculate the time taken to overtake
- Using the formula for time \( t \):
\[ t = \frac{d}{v_{relative}} \]
- Substituting the values we have:
\[ t = \frac{6 \, \text{m}}{10 \, \text{m/s}} = 0.6 \, \text{s} \]

### Final Answer
The time taken by the first car to pass the second car is **0.6 seconds**.

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