Question 49: Solution
1. Analyzing Graph Coordinates
We identify the moment of gear shift by finding clear intersection points on the provided velocity-time graph. We observe two consecutive clear points:
- Point A ($t=30$): The curve passes exactly halfway between $v=20$ and $v=30$. Thus, $v_{30} = 25 \, \text{m/s}$.
- Point B ($t=40$): The curve passes exactly on the grid line for $v=30$. Thus, $v_{40} = 30 \, \text{m/s}$.
2. Verification via Slope
The question states that the graph can be treated as straight lines in 10 s intervals. Let’s verify the acceleration in this specific interval:
$$ a_{30-40} = \frac{v_{40} – v_{30}}{t_{40} – t_{30}} $$
$$ a_{30-40} = \frac{30 – 25}{40 – 30} = \frac{5}{10} = 0.5 \, \text{m/s}^2 $$
Key Insight: The graph shows a distinct linear segment starting exactly at $t=30 \, \text{s}$. This confirms $t=30$ is a critical node in the motion profile defined by the problem setter.
3. Conclusion
The gear shift occurs at the point verified by the coordinates and the slope analysis, as the graph can be retraced only when the acceleration is $$ 0.5 \, \text{m/s}^2$$
Correct Answer: (c) 30 s