### Solution:
#### Numerical Problem a:
Problem: A car covers a distance of 240 km in 4 hours. Calculate its average speed.
Step-by-Step Solution:
1. Identify the known values:
- Distance covered by the car: [tex]\( d = 240 \)[/tex] kilometers
- Time taken by the car: [tex]\( t = 4 \)[/tex] hours
2. Recall the formula for average speed:
[tex]\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \][/tex]
3. Substitute the known values into the formula:
[tex]\[ \text{Average Speed} = \frac{240 \text{ km}}{4 \text{ hours}} \][/tex]
4. Perform the division:
[tex]\[ \text{Average Speed} = 60 \text{ km/h} \][/tex]
Final Answer:
- The average speed of the car is [tex]\( 60 \)[/tex] km/h.
#### Numerical Problem b:
Problem: A train accelerates from rest at a rate of 2 m/s² for 10 seconds. Calculate its final velocity.
Step-by-Step Solution:
1. Identify the known values:
- Initial velocity ([tex]\( u \)[/tex]) of the train: [tex]\( u = 0 \)[/tex] m/s (since it starts from rest)
- Acceleration ([tex]\( a \)[/tex]) of the train: [tex]\( a = 2 \)[/tex] m/s²
- Time duration ([tex]\( t \)[/tex]) for which the train accelerates: [tex]\( t = 10 \)[/tex] seconds
2. Recall the formula for final velocity when an object is under constant acceleration:
[tex]\[ v = u + at \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity
- [tex]\( u \)[/tex] is the initial velocity
- [tex]\( a \)[/tex] is the acceleration
- [tex]\( t \)[/tex] is the time
3. Substitute the known values into the formula:
[tex]\[ v = 0 \text{ m/s} + (2 \text{ m/s}^2 \times 10 \text{ s}) \][/tex]
4. Perform the multiplication:
[tex]\[ v = 0 \text{ m/s} + 20 \text{ m/s} \][/tex]
5. Simplify the expression:
[tex]\[ v = 20 \text{ m/s} \][/tex]
Final Answer:
- The final velocity of the train is [tex]\( 20 \)[/tex] m/s.
### Summary:
- The average speed of the car in problem a is [tex]\( 60 \)[/tex] km/h.
- The final velocity of the train in problem b is [tex]\( 20 \)[/tex] m/s.
