📄 8th Grade Math (Algebra I): Distance, Speed, and Time Worksheet
📌 1. True / False
1. Distance is calculated by multiplying speed and time.
2. If you travel at a constant speed, your average speed will be different from your instantaneous speed.
3. Speed is a measure of how fast an object is moving.
4. Time is typically measured in units like meters or kilometers.
5. To find time, you divide distance by speed.
✏️ 2. Fill in the Blanks
1. The formula relating distance, speed, and time is Distance = Speed \( \times \) .
2. is the rate at which an object covers a certain distance.
3. If a car travels 100 miles in 2 hours, its average speed is miles per hour.
4. To calculate the time taken, you can use the formula Time = Distance \( \div \) .
5. The total path covered by an object is called .
🔗 3. Matching
« The total length of the path traveled by an object.
« The rate at which an object covers distance.
« The duration for which an action, process, or condition exists or continues.
« Total distance divided by total time taken.
« \( d = s \times t \)
✍️ 4. Short Answer Questions
1. What are the standard units for distance, speed, and time in the metric system?
💡 Suggested Answer: Distance: meters (m) or kilometers (km). Speed: meters per second (m/s) or kilometers per hour (km/h). Time: seconds (s) or hours (h).
2. Explain the difference between speed and velocity.
💡 Suggested Answer: Speed is a scalar quantity that only describes how fast an object is moving. Velocity is a vector quantity that describes both the speed and the direction of an object's motion.
🎯 5. Multiple Choice
1. A train travels 240 miles in 3 hours. What is its average speed?
2. How long will it take a car to travel 350 kilometers if it maintains a speed of 70 km/h?
3. If a runner completes a 10-kilometer race in 50 minutes, what is their average speed in kilometers per minute?
📝 6. Open-Ended Questions
1. A cyclist rides for 4 hours at an average speed of 15 miles per hour. How far did the cyclist travel?
💡 Solution Steps:
The formula for distance is Distance = Speed \( \times \) Time.
Given:
Speed = 15 miles per hour
Time = 4 hours
Distance = 15 mph \( \times \) 4 hours
Distance = 60 miles
The cyclist traveled 60 miles.
2. A bus leaves the station and travels at a constant speed of 60 km/h. Another bus leaves the same station 1 hour later and travels at a constant speed of 80 km/h in the same direction. How long will it take the second bus to catch up to the first bus?
💡 Solution Steps:
Let \( t \) be the time in hours that the second bus travels until it catches up.
The first bus travels for \( t + 1 \) hours.
Distance covered by the first bus = Speed \( \times \) Time = \( 60(t + 1) \) km.
Distance covered by the second bus = Speed \( \times \) Time = \( 80t \) km.
When the second bus catches up, their distances will be equal.
So, \( 60(t + 1) = 80t \)
Distribute the 60: \( 60t + 60 = 80t \)
Subtract \( 60t \) from both sides: \( 60 = 20t \)
Divide by 20: \( t = \frac{60}{20} \)
\( t = 3 \) hours.
It will take the second bus 3 hours to catch up to the first bus.
3. A car travels from Town A to Town B, a distance of 180 miles, at an average speed of 45 mph. It then returns from Town B to Town A at an average speed of 60 mph. What is the total time taken for the entire round trip?
💡 Solution Steps:
First, calculate the time taken to travel from Town A to Town B.
Time = Distance \( \div \) Speed
Time (A to B) = 180 miles \( \div \) 45 mph = 4 hours.
Next, calculate the time taken to travel from Town B to Town A.
Time (B to A) = 180 miles \( \div \) 60 mph = 3 hours.
Finally, calculate the total time for the round trip.
Total Time = Time (A to B) + Time (B to A)
Total Time = 4 hours + 3 hours = 7 hours.
The total time taken for the entire round trip is 7 hours.
Name Surname: .................................. Date: .... / .... / 202...
Distance, Speed, and Time Worksheet
SCORE
A. True (T) / False (F)
( .... )
Distance is calculated by multiplying speed and time.
( .... )
If you travel at a constant speed, your average speed will be different from your instantaneous speed.
( .... )
Speed is a measure of how fast an object is moving.
( .... )
Time is typically measured in units like meters or kilometers.
( .... )
To find time, you divide distance by speed.
B. Fill in the Blanks
1)
The formula relating distance, speed, and time is Distance = Speed \( \times \) .....................
2)
.................... is the rate at which an object covers a certain distance.
3)
If a car travels 100 miles in 2 hours, its average speed is .................... miles per hour.
4)
To calculate the time taken, you can use the formula Time = Distance \( \div \) .....................
5)
The total path covered by an object is called .....................
C. Matching Concepts
( .... )
The total length of the path traveled by an object.
- Time
( .... )
The rate at which an object covers distance.
- Distance
( .... )
The duration for which an action, process, or condition exists or continues.
- Speed
( .... )
Total distance divided by total time taken.
- Average Speed
( .... )
\( d = s \times t \)
- Formula for Distance
D. Short Answer Questions
1)
What are the standard units for distance, speed, and time in the metric system?
2)
Explain the difference between speed and velocity.
E. Multiple Choice Questions
1)
A train travels 240 miles in 3 hours. What is its average speed?
A) 60 mphB) 80 mphC) 70 mphD) 90 mph
2)
How long will it take a car to travel 350 kilometers if it maintains a speed of 70 km/h?
A) 4 hoursB) 6 hoursC) 5 hoursD) 7 hours
3)
If a runner completes a 10-kilometer race in 50 minutes, what is their average speed in kilometers per minute?
A) 0.2 km/minB) 0.5 km/minC) 2 km/minD) 5 km/min
F. Open-Ended Questions
1)
A cyclist rides for 4 hours at an average speed of 15 miles per hour. How far did the cyclist travel?
2)
A bus leaves the station and travels at a constant speed of 60 km/h. Another bus leaves the same station 1 hour later and travels at a constant speed of 80 km/h in the same direction. How long will it take the second bus to catch up to the first bus?
3)
A car travels from Town A to Town B, a distance of 180 miles, at an average speed of 45 mph. It then returns from Town B to Town A at an average speed of 60 mph. What is the total time taken for the entire round trip?