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Two bodies starts moving from same point...

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 ?

A

6 s

B

8 s

C

12 s

D

10 s

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will use the concept of relative motion. ### Step-by-Step Solution: 1. **Identify the velocities of the two bodies**: - Let the velocity of the first body (v1) be 6 m/s. - Let the velocity of the second body (v2) be 10 m/s. 2. **Determine the relative velocity**: - The relative velocity of the second body with respect to the first body can be calculated as: \[ v_{rel} = v_2 - v_1 = 10 \, \text{m/s} - 6 \, \text{m/s} = 4 \, \text{m/s} \] 3. **Set the relative distance**: - We want to find out when the separation between the two bodies becomes 40 meters. This is our relative distance (d). - Therefore, \( d = 40 \, \text{m} \). 4. **Use the formula for time**: - The time (t) taken for the relative distance to be covered can be calculated using the formula: \[ t = \frac{d}{v_{rel}} \] - Substituting the values we have: \[ t = \frac{40 \, \text{m}}{4 \, \text{m/s}} = 10 \, \text{s} \] 5. **Conclusion**: - The time after which the separation between the two bodies becomes 40 meters is **10 seconds**.
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