A girl is preparing for her first marathon by running on a straight road. Class 9
A girl is preparing for her first marathon by running on a straight road. Class 9
Question 1.
A girl is preparing for her first marathon by running on a straight road. She uses a smartwatch to calculate her running speed at different intervals. The graph depicts her velocity versus time. Estimate the running distance based on the graph. Class 9
Answer:
The running distance = area enclosed under the velocity-time graph and the time axis.
Estimating area:
Phase 1 (0 to 2 h):
Approximately a trapezium with parallel sides 5.0 and 7.5 km h-1, width 2 h:
Area1 = 1/2 × (5.0 + 7.5) × 2
= 1/2 × 12.5 × 2 = 12.5 km
Phase 2 (2 to 4 h):
Rectangle with height 7.5 km h-1, width 2 h:
Area2 = 7.5 × 2 = 15 km
Phase 3 (4 to 6 h):
Approximately a trapezium with parallel sides 7.5 and some lower value. If it decreases linearly to about 5 km h-1:
Area3 = 1/2 × (7.5 + 5.0) × 2
= 14 × 12.5 × 2
= 12.5 km
Estimated total running distance ≈ 12.5 + 15 + 12.5 = 40 km