Let's solve these problems step-by-step.
Problem 1: Toy Train Distance Traveled
1. Identify the given values:
- Average speed of the toy train, [tex]\( v = 0.25 \)[/tex] meters per second (m/s)
- Time taken, [tex]\( t = 4.00 \)[/tex] minutes
2. Convert the time from minutes to seconds because the speed is given in meters per second. There are 60 seconds in one minute.
[tex]\( t = 4.00 \)[/tex] minutes [tex]\( \times 60 \)[/tex] seconds/minute
[tex]\( t = 240 \)[/tex] seconds
3. Now use the formula for distance when speed and time are given. The formula is:
[tex]\( \text{distance} = \text{speed} \times \text{time} \)[/tex]
4. Apply the values to the formula:
[tex]\( \text{distance} = 0.25 \)[/tex] m/s [tex]\( \times 240 \)[/tex] s
5. Calculate the distance the toy train travels:
[tex]\( \text{distance} = 60 \)[/tex] meters
So, the toy train will travel 60 meters in 4 minutes.
Problem 2: Student's Car Average Speed
1. Identify the given values:
- Distance traveled by the car, [tex]\( d = 10.0 \)[/tex] kilometers (km)
- Time taken, [tex]\( t = 30.0 \)[/tex] minutes
2. Convert the time from minutes to hours because the standard unit of speed is kilometers per hour (km/h). There are 60 minutes in one hour.
[tex]\( t = 30.0 \)[/tex] minutes [tex]\( \times \frac{1}{60} \)[/tex] hours/minute
[tex]\( t = 0.5 \)[/tex] hours
3. Now use the formula for speed when distance and time are given. The formula is:
[tex]\( \text{speed} = \frac{\text{distance}}{\text{time}} \)[/tex]
4. Apply the values to the formula:
[tex]\( \text{speed} = \frac{10.0 \text{ km}}{0.5 \text{ hours}} \)[/tex]
5. Calculate the student's car average speed:
[tex]\( \text{speed} = 20.0 \)[/tex] km/h
So, the student's average speed was 20.0 kilometers per hour (km/h).
