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, \(\( v = 0.25 \)\) meters per second (m/s)
- Time taken, \(\( t = 4.00 \)\) 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.
\(\( t = 4.00 \)\) minutes \(\( \times 60 \)\) seconds/minute
\(\( t = 240 \)\) seconds
3. Now use the formula for distance when speed and time are given. The formula is:
\(\( \text{distance} = \text{speed} \times \text{time} \)\)
4. Apply the values to the formula:
\(\( \text{distance} = 0.25 \)\) m/s \(\( \times 240 \)\) s
5. Calculate the distance the toy train travels:
\(\( \text{distance} = 60 \)\) 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, \(\( d = 10.0 \)\) kilometers (km)
- Time taken, \(\( t = 30.0 \)\) 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.
\(\( t = 30.0 \)\) minutes \(\( \times \frac{1}{60} \)\) hours/minute
\(\( t = 0.5 \)\) hours
3. Now use the formula for speed when distance and time are given. The formula is:
\(\( \text{speed} = \frac{\text{distance}}{\text{time}} \)\)
4. Apply the values to the formula:
\(\( \text{speed} = \frac{10.0 \text{ km}}{0.5 \text{ hours}} \)\)
5. Calculate the student's car average speed:
\(\( \text{speed} = 20.0 \)\) km/h
So, the student's average speed was 20.0 kilometers per hour (km/h).
