Instructions
This worksheet focuses on calculating speed, distance, and time (SDT) using equine scenarios. Please follow these steps:
- Review the key formulas provided below.
- Complete the tasks in order, showing your work when necessary.
- Pay close attention to the units required for your final answer.
The Formulas (SDT Triangle)
| Calculation | Formula |
|---|---|
| Speed (S) | Distance / Time (S = D/T) |
| Distance (D) | Speed × Time (D = S × T) |
| Time (T) | Distance / Speed (T = D / S) |
Remember: 1 kilometer (km) = 1,000 meters (m); 1 hour = 60 minutes.
Section 1: The Paddock Warm-Up (Basic Calculations)
Use the SDT formulas to fill in the missing value in the table. Ensure your units match the column headings.
| Speed | Distance | Time | Calculation Example |
|---|---|---|---|
| 15 km/h | 30 km | 2 hours | 30 km / 15 km/h = 2 h |
| 18 km/h | 9 km | ||
| 6 m/s | 15 seconds | ||
| 120 meters | 24 seconds | ||
| 20 km/h | 5 km | ||
| 10 m/s | 1 km (1000m) |
Section 2: Unit Conversion Challenge
In equine sports, speeds are often measured in meters per second (m/s) or kilometers per hour (km/h). Complete the following conversions.
Hint: To go from m/s to km/h, multiply by 3.6. To go from km/h to m/s, divide by 3.6.
-
A racing Quarter Horse runs at a top speed of 22 m/s. What is its speed in kilometers per hour (km/h)?
Show your work:
Answer: __ km/h
-
A trail pony maintains a steady speed of 10.8 km/h. What is this speed in meters per second (m/s)?
Show your work:
Answer: __ m/s
Section 3: Endurance Riding Scenarios (Problem Solving)
Solve the following word problems. Ensure your final answer includes the correct units.
-
The Training Run: A rider takes their Arabian horse on a long training run. The horse maintains an average speed of 16 km/h. If the horse travels for 3 hours and 45 minutes, what is the total distance covered?
(Remember to convert 45 minutes into a decimal fraction of an hour before calculating.)
Total Distance: __
-
The Veterinary Check: During a critical care situation, a veterinarian needs to measure a horse's recovery speed. The vet marks a 50-meter track. The horse covers the 50 meters in exactly 7.5 seconds. What is the horse's speed in meters per second (m/s)?
Speed: __
-
The Show Circuit: A team needs to transport a horse 480 kilometers to the next show. They plan to travel at an average speed of 80 km/h, but they must stop for two 30-minute breaks to walk the horse. How long will the entire trip take, from start to finish (travel time + breaks)?
Total Trip Time: __
Section 4: The Kentucky Derby Challenge (Advanced)
The Kentucky Derby is approximately 1.25 miles long. The fastest winning time recorded (Secretariat, 1973) was 1 minute and 59.4 seconds (or 119.4 seconds total).
Challenge Question: Calculate Secretariat's average speed in miles per hour (mph) during the race.
Hint:
- Time (T) in hours = 119.4 seconds / 3600 seconds/hour.
- Speed (S) = Distance (1.25 miles) / Time (T in hours).
Average Speed: __ mph
Answer Key
Section 1: The Paddock Warm-Up
| Speed | Distance | Time | Calculation |
|---|---|---|---|
| 18 km/h | 9 km | 0.5 hours (30 min) | T = 9 / 18 = 0.5 h |
| 6 m/s | 90 meters | 15 seconds | D = 6 * 15 = 90 m |
| 5 m/s | 120 meters | 24 seconds | S = 120 / 24 = 5 m/s |
| 20 km/h | 5 km | 0.25 hours (15 min) | T = 5 / 20 = 0.25 h |
| 10 m/s | 1 km (1000m) | 100 seconds | T = 1000 / 10 = 100 s |
Section 2: Unit Conversion Challenge
- 22 m/s * 3.6 = 79.2 km/h
- 10.8 km/h / 3.6 = 3 m/s
Section 3: Endurance Riding Scenarios
- 3 hours 45 minutes = 3.75 hours. D = 16 km/h * 3.75 h = 60 km
- Speed = 50 meters / 7.5 seconds = 6.67 m/s (rounded)
- Travel time T = 480 km / 80 km/h = 6 hours. Total breaks = 30 min + 30 min = 1 hour. Total Trip Time = 6 + 1 = 7 hours
Section 4: The Kentucky Derby Challenge
- Time in hours = 119.4 / 3600 ≈ 0.033167 hours
- S = 1.25 miles / 0.033167 hours = 37.69 mph (rounded)