Answer :
To solve the problem of finding the relative velocity of car A with respect to car B, we can follow a detailed, step-by-step approach.
### Step-by-Step Solution
1. Understand the Given Information:
- Car A has a velocity of [tex]\( 30 \ \text{m/s} \)[/tex].
- Car B has a velocity of [tex]\( 25 \ \text{m/s} \)[/tex].
- Both cars are moving in the same direction and start from the same place at the same time.
2. Define Relative Velocity:
- The relative velocity of one object with respect to another is defined as the velocity of the first object minus the velocity of the second object. In this case, we need to find the velocity of car A with respect to car B.
3. Calculate the Relative Velocity:
- For two objects moving in the same direction, the relative velocity [tex]\( V_{\text{relative}} \)[/tex] is given by:
[tex]\[ V_{\text{relative}} = V_A - V_B \][/tex]
where:
- [tex]\( V_A \)[/tex] is the velocity of car A
- [tex]\( V_B \)[/tex] is the velocity of car B
4. Substitute the Given Values:
- [tex]\( V_A = 30 \ \text{m/s} \)[/tex]
- [tex]\( V_B = 25 \ \text{m/s} \)[/tex]
- Therefore,
[tex]\[ V_{\text{relative}} = 30 \ \text{m/s} - 25 \ \text{m/s} \][/tex]
5. Perform the Calculation:
[tex]\[ V_{\text{relative}} = 5 \ \text{m/s} \][/tex]
### Conclusion
The relative velocity of car A with respect to car B after 1 second is [tex]\( \mathbf{5 \ \text{m/s}} \)[/tex]. This means that from the perspective of someone in car B, car A appears to be moving forward at a speed of [tex]\( \mathbf{5 \ \text{m/s}} \)[/tex].
### Step-by-Step Solution
1. Understand the Given Information:
- Car A has a velocity of [tex]\( 30 \ \text{m/s} \)[/tex].
- Car B has a velocity of [tex]\( 25 \ \text{m/s} \)[/tex].
- Both cars are moving in the same direction and start from the same place at the same time.
2. Define Relative Velocity:
- The relative velocity of one object with respect to another is defined as the velocity of the first object minus the velocity of the second object. In this case, we need to find the velocity of car A with respect to car B.
3. Calculate the Relative Velocity:
- For two objects moving in the same direction, the relative velocity [tex]\( V_{\text{relative}} \)[/tex] is given by:
[tex]\[ V_{\text{relative}} = V_A - V_B \][/tex]
where:
- [tex]\( V_A \)[/tex] is the velocity of car A
- [tex]\( V_B \)[/tex] is the velocity of car B
4. Substitute the Given Values:
- [tex]\( V_A = 30 \ \text{m/s} \)[/tex]
- [tex]\( V_B = 25 \ \text{m/s} \)[/tex]
- Therefore,
[tex]\[ V_{\text{relative}} = 30 \ \text{m/s} - 25 \ \text{m/s} \][/tex]
5. Perform the Calculation:
[tex]\[ V_{\text{relative}} = 5 \ \text{m/s} \][/tex]
### Conclusion
The relative velocity of car A with respect to car B after 1 second is [tex]\( \mathbf{5 \ \text{m/s}} \)[/tex]. This means that from the perspective of someone in car B, car A appears to be moving forward at a speed of [tex]\( \mathbf{5 \ \text{m/s}} \)[/tex].
