Solved Examples: Impulse and Momentum in Car Accidents

📚 Quick Study Guide

• ⚖️ Momentum: A measure of mass in motion. Formula: $p = mv$, where $p$ is momentum, $m$ is mass, and $v$ is velocity.
• 💥 Impulse: The change in momentum. It's equal to the force applied over a period of time. Formula: $J = F\Delta t$, where $J$ is impulse, $F$ is force, and $\Delta t$ is the time interval. Also, $J = \Delta p$.
• 🚗 Impulse-Momentum Theorem: States that the impulse on an object is equal to the change in its momentum. $F\Delta t = m(v_f - v_i)$, where $v_f$ is the final velocity and $v_i$ is the initial velocity.
• 🚧 Conservation of Momentum: In a closed system, the total momentum remains constant if no external forces act. $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$.

Practice Quiz

1. A 1500 kg car is traveling at 20 m/s. What is its momentum?
   1. A) 15,000 kg m/s
   2. B) 30,000 kg m/s
   3. C) 75 kg m/s
   4. D) 150 kg m/s
2. A car crashes into a wall and comes to a complete stop. Which statement is TRUE regarding the impulse experienced by the car?
   1. A) The impulse is zero because the final velocity is zero.
   2. B) The impulse is equal to the car's initial momentum.
   3. C) The impulse is equal to the car's final momentum.
   4. D) The impulse cannot be determined without knowing the impact time.
3. A 2000 kg truck traveling at 10 m/s hits a stationary 1000 kg car. They stick together after the collision. What is their combined velocity immediately after the collision?
   1. A) 3.33 m/s
   2. B) 6.67 m/s
   3. C) 13.33 m/s
   4. D) 20 m/s
4. A force of 5000 N is applied to a car for 0.1 seconds during a collision. What is the impulse experienced by the car?
   1. A) 50 Ns
   2. B) 500 Ns
   3. C) 5000 Ns
   4. D) 50,000 Ns
5. A car's momentum changes from 10,000 kg m/s to 5,000 kg m/s in 2 seconds during braking. What is the average force exerted on the car?
   1. A) 2,500 N
   2. B) 5,000 N
   3. C) 7,500 N
   4. D) 10,000 N
6. Two cars of equal mass collide head-on. Car A is traveling at +15 m/s, and Car B is traveling at -15 m/s. If the collision is perfectly elastic, what is the velocity of Car A after the collision?
   1. A) +15 m/s
   2. B) -15 m/s
   3. C) 0 m/s
   4. D) +30 m/s
7. Which of the following scenarios best demonstrates the principle of conservation of momentum?
   1. A) A car accelerating from rest.
   2. B) A car braking to a stop.
   3. C) Two cars colliding on an icy road.
   4. D) A car driving around a curve at constant speed.