UPSC NDA I 2026 General Ability Paper

1. Concept:The area under a force-time ($F-t$) graph gives the impulse, which is equal to the change in momentum of the object ($\Delta p = m \Delta v$).2. Explanation:• The shape of the graph is a trapezium. We can calculate its area to find the total impulse.• The parallel sides of the trapezium are the base (from $t = 0$ to $t = 25$) and the top side (from $t = 5$ to $t = 20$).• Length of the base = $25 - 0 = 25\text{ s}$• Length of the top side = $20 - 5 = 15\text{ s}$• Height of the trapezium = $20\text{ N}$• Calculate the area (Impulse):$$\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$$$$\text{Area} = \frac{1}{2} \times (25 + 15) \times 20 = \frac{1}{2} \times 40 \times 20 = 400\text{ N s}$$• The change in momentum is $\Delta p = 400\text{ kg m/s}$.• Using the relation $\Delta p = m(v_f - v_i)$ and assuming the object starts from rest ($v_i = 0$):$$400 = 10 \times v_f$$$$v_f = \frac{400}{10} = 40\text{ m/s}$$3. Answer:40 m/s