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