Two bodies starts moving from same point along straight line with velocities ` v_(1) = 6 m//s " and " v_(2) = 10 m//s `
simultaneously. After what time the separation becomes 40 m ?

Options

A. 6 s
B. 8 s
C. 12 s
D. 10 s

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We have two bodies moving from the same point with different velocities. We need to find the time after which the separation between them becomes 40 meters.

### Step 2: Define the Variables
Let:
- \( v_1 = 6 \, \text{m/s} \) (velocity of the first body)
- \( v_2 = 10 \, \text{m/s} \) (velocity of the second body)
- \( t \) = time after which the separation is 40 meters

### Step 3: Calculate Distances Traveled
The distance traveled by each body after time \( t \) can be calculated using the formula:
- Distance = Velocity × Time

For the first body:
\[ d_1 = v_1 \cdot t = 6 \cdot t \]

For the second body:
\[ d_2 = v_2 \cdot t = 10 \cdot t \]

### Step 4: Set Up the Equation for Separation
The separation between the two bodies after time \( t \) is given by:
\[ \text{Separation} = d_2 - d_1 \]

We know that the separation is 40 meters:
\[ d_2 - d_1 = 40 \]

Substituting the expressions for \( d_1 \) and \( d_2 \):
\[ 10t - 6t = 40 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ 4t = 40 \]

### Step 6: Solve for Time \( t \)
Now, divide both sides by 4:
\[ t = \frac{40}{4} = 10 \, \text{seconds} \]

### Conclusion
The time after which the separation between the two bodies becomes 40 meters is \( t = 10 \) seconds.

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