Comprehensive study of time, speed, and distance calculations for CBSE Class 11 Applied Mathematics, covering uniform motion, unit conversions, and step-by-step problem solving.
In Applied Mathematics, the relationship between distance (d), speed (v), and time (t) forms the bedrock of kinematics problems. Assuming constant speed, the distance traveled is directly proportional to the time taken. It is essential to ensure unit consistency (e.g., converting km/h to m/s) before performing calculations.
• Step 1: Convert speed from km/h to km/min: 72 km/h = 72/60 km/min = 1.2 km/min.
• Step 2: Use the formula Distance = Speed × Time.
• Step 3: Multiply: 1.2 km/min × 20 min = 24 km.
Answer: The car covers a distance of 24 km.
Often, data provided in exam questions involve mixed units. To convert km/h to m/s, multiply by 5/18. Conversely, to convert m/s to km/h, multiply by 18/5. When calculating time for a journey with varying speeds, one must calculate total distance and total time separately before finding the average.
• Step 1: Calculate speed in m/s: 150m / 10s = 15 m/s.
• Step 2: Convert to km/h: 15 × (18/5) = 54 km/h.
• Step 3: Calculate time for 5 km: Time = Distance / Speed = 5 km / 54 km/h = 5/54 hours.
• Step 4: Convert to minutes: (5/54) × 60 = 5.55 minutes.
Answer: The speed is 54 km/h, and the time taken to cover 5 km is approximately 5.55 minutes.