The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. The graph shows V starts at 0, rises linearly to 1 m/s at t=2 s, stays constant at 1 m/s from t=2 to t=4 s, then decreases linearly back to -2 m/s at t=7 s. At the end of 7 seconds, how will the odometer reading increase by (in m)?
A. 0
B. 3
C. 4
D. 5
GATE 2016 · General Aptitude · Speed Time Distance · medium
Answer: The odometer reading increases by approximately 5 m (Answer D = 5).
Identify the three velocity segments from the graph: Segment A: 0 to 2 s, V rises from 0 to 1 m/s (triangle). Segment B: 2 to 4 s, V constant at 1 m/s (rectangle). Segment C: 4 to 7 s, V decreases from 1 to -2 m/s (crosses zero at t=5 s).
Compute area of segment A (triangle, 0-2 s): Area_A = (1/2)(2)(1) = 1 m. This is 1 m of forward distance.
Compute area of segment B (rectangle, 2-4 s): Area_B = (2)(1) = 2 m. This is 2 m of forward distance.
Compute area of segment C (4-7 s with sign change): V decreases linearly from 1 m/s at t=4 to -2 m/s at t=7. Rate of change = (-2-1)/3 = -1 m/s^2. Zero crossing at t = 4 + 1/1 = 5 s. Forward part (4 to 5 s): triangle with base 1 and height 1, area = 0.5 m. Backward part (5 to 7 s): triangle with base 2 and height 2, area = 2 m. Segment C total = 0.5 + 2 = 2.5 m.
Sum all segments: Total = 1 + 2 + 2.5 = 5.5 m. The closest answer is D = 5 m.