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 break it down into clear steps:

### Step 1: Determine the total distance to be covered
The first car, which is 2 meters long, needs to completely pass the second car, which is 4 meters long. Therefore, the total distance that the first car must travel to completely overtake the second car is the sum of the lengths of both cars.

\[ \text{Total distance} = \text{Length of Car 1} + \text{Length of Car 2} = 2 \, \text{m} + 4 \, \text{m} = 6 \, \text{m} \]

### Step 2: Calculate the relative velocity
The first car is traveling at 30 m/s, and the second car is traveling at 20 m/s. Since both cars are moving in the same direction, we can find the relative velocity of the first car with respect to the second car by subtracting the speed of the second car from the speed of the first car.

\[ \text{Relative velocity} = \text{Velocity of Car 1} - \text{Velocity of Car 2} = 30 \, \text{m/s} - 20 \, \text{m/s} = 10 \, \text{m/s} \]

### Step 3: Calculate the time taken to overtake
Now that we have the total distance (6 m) and the relative velocity (10 m/s), we can use the formula for time, which is given by:

\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} \]

Substituting the values we have:

\[ \text{Time} = \frac{6 \, \text{m}}{10 \, \text{m/s}} = 0.6 \, \text{s} \]

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

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