AP Physics 1 Questions on Impulse as Area Under a Force-Time Graph

📚 Quick Study Guide

• 📈 Impulse Definition: Impulse ($J$) is the change in momentum of an object. It's a vector quantity.
• 🍎 Impulse and Momentum: Impulse is equal to the change in momentum: $J = \Delta p = m\Delta v$, where $m$ is mass and $\Delta v$ is the change in velocity.
• 🧭 Force and Impulse: Impulse is also defined as the integral of force with respect to time: $J = \int F dt$.
• 📐 Area Under the Curve: On a Force vs. Time (F-t) graph, the area under the curve represents the impulse.
• 🧮 Constant Force: If the force is constant, the impulse is simply $J = F\Delta t$.
• 💡 Varying Force: If the force varies with time, you need to find the area under the curve using geometry (e.g., triangles, rectangles) or integration.
• ➕ Net Impulse: The net impulse is the vector sum of all impulses acting on an object.

Practice Quiz

1. A 2 kg object experiences a force that varies with time as shown in the graph. What is the impulse on the object between t = 0 s and t = 4 s if the graph forms a rectangle with height 10 N and width 4 s?
   A) 10 Ns
   B) 20 Ns
   C) 40 Ns
   D) 80 Ns
2. The area under a Force vs. Time graph represents:
   A) Change in kinetic energy
   B) Work done
   C) Impulse
   D) Average velocity
3. A constant force of 5 N is applied to an object for 3 seconds. What is the impulse on the object?
   A) 5 Ns
   B) 8 Ns
   C) 15 Ns
   D) 20 Ns
4. An object experiences an impulse of 20 Ns. If the interaction lasted for 5 seconds, what was the average force applied?
   A) 4 N
   B) 5 N
   C) 10 N
   D) 25 N
5. The graph of a force acting on an object shows a triangle with a base of 6 s and a height of 12 N. What is the impulse imparted to the object?
   A) 12 Ns
   B) 36 Ns
   C) 72 Ns
   D) 84 Ns
6. A ball experiences a force described by $F(t) = 2t + 3$ (in Newtons), where $t$ is in seconds. What is the impulse on the ball from t = 0 to t = 2 seconds?
   A) 4 Ns
   B) 6 Ns
   C) 10 Ns
   D) 14 Ns
7. A 5 kg object's velocity changes from 2 m/s to 6 m/s due to an applied force. What is the impulse on the object?
   A) 4 Ns
   B) 10 Ns
   C) 20 Ns
   D) 30 Ns