The time taken/ distance covered from the given data

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.

Fundamental Relationship of Motion

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.

d = v × t; v = d/t; t = d/v
Example 1: A car travels at a constant speed of 72 km/h. How much distance will it cover in 20 minutes?
Show Step-by-Step Solution

• 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.

Unit Conversion and Average Speed

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.

Average Speed = Total Distance / Total Time
Example 1: A train covers 150 meters in 10 seconds. Calculate its speed in km/h and the time taken to cover 5 km.
Show Step-by-Step Solution

• 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.