AQA AS Level Physics Paper 2, June 2025: Question 13

✅ Correct Answer: Option D

• Time to reach terminal speed: time for X > time for Y
• Upward force at terminal speed: upward force on X > upward force on Y

🔧 Step-by-Step Physics Breakdown

1. 1. Upward force at terminal speed:
   At terminal speed, acceleration a = 0 , meaning resultant force F_net = 0 .
   Therefore: Upward Force (Drag) = Weight = mg .
   Since m_X (120 kg) > m_Y (90 kg) :
   Drag_X = 120 × 9.81 = 1180 N
   Drag_Y = 90 × 9.81 = 883 N
   ⇒ Upward force on X > upward force on Y.
2. 2. Time taken to reach terminal speed:
   Because skydiver X requires a larger upward drag to balance their larger weight, they must attain a higher terminal speed (since drag increases with speed: D ∝ v² ).
   Both skydivers start with the same initial acceleration ( g = 9.81 m s⁻² ). As speed builds, drag increases and acceleration decreases towards zero.
   Because X must accelerate up to a much higher velocity, X takes a longer time to reach equilibrium.
   ⇒ Time for X > time for Y.

💡 Key Knowledge

• Equilibrium condition: At terminal velocity, forces are balanced. Drag force is equal and opposite to weight ( W = mg ).
• Dependence on speed: Air resistance increases as speed increases. A heavier skydiver needs more air resistance to balance weight, requiring a higher speed.
• Velocity-time profile: Both curves start with initial gradient g . The heavier object continues accelerating after the lighter object's acceleration has already decayed to zero, taking longer to plateau.

🧠 Exam Technique & Elimination

• Split the table into two columns:
  • Evaluate the Upward force column first—it is simpler because Upward Force = mg . Since 120 kg > 90 kg , the upward force on X must be greater than on Y.
  • This immediately eliminates B and C.
• Decide between A and D: Ask yourself: "Who has further to accelerate?" Skydiver X must reach a higher speed, so they accelerate for a longer period. This confirms D.

❌ Common Errors & Pitfalls

• Thinking upward forces are equal: Believing that "terminal velocity" means drag reaches a fixed universal value. Drag always matches the specific object's weight.
• Ignoring air resistance kinematics: Assuming heavier objects fall faster, so they must "reach terminal speed quicker". While they do fall faster, they take more time to reach their final speed because that final speed is significantly higher.
• Confusing resultant force with drag force: The resultant force is zero for both skydivers at terminal speed, but the upward drag force itself is distinctly non-zero and directly proportional to weight.