# Problem Bank

## 537 problems across 27 topics

The full training library. Filter by field, topic, difficulty, or search for specific concepts.

### Topics
- electricity: 60
- magnetism: 41
- mechanics: 274
- modern physics: 60
- optics: 41
- thermodynamics: 41
- waves: 20

### Kinematics 1D
1. A car accelerates uniformly from rest to 27 m/s in 6.0 s. What is the car's acceleration? **(numerical)**
2. A stone is dropped from rest from the top of a 45 m tall building. Ignoring air resistance, how long does it take to reach the ground? Use g = 9.8 m/s². **(numerical)**
3. A subway train starts from rest and accelerates at 1.2 m/s² for 14 s. It then runs at constant speed for 70 s and finally decelerates at 1.6 m/s² until it stops. What is the total distance traveled? **(multi-step)**
4. A ball is thrown vertically upward with an initial speed of 20 m/s from the edge of a 50 m high cliff. What is the speed of the ball when it hits the ground below? Use g = 9.8 m/s². **(numerical)**
5. The position of a particle as a function of time is given by x(t) = 4t² - 2t + 1 (meters, with t in seconds). Find (a) the velocity at t = 3 s, (b) the acceleration, and (c) the position when the velocity is zero. **(numerical)**
6. Two cars start from the same point at the same time. Car A accelerates from rest at 3.0 m/s², while Car B moves at a constant velocity of 18 m/s. (a) At what time does Car A catch up to Car B? (b) How far from the starting point does this occur? **(multi-step)**
7. A car traveling at 30 m/s applies its brakes and decelerates uniformly at 5.0 m/s². How far does the car travel before coming to a complete stop? **(numerical)**
8. A velocity-time graph shows a particle starting at 10 m/s, linearly decreasing to 0 m/s at t = 5 s, then linearly increasing in the negative direction to -10 m/s at t = 10 s. What is the total displacement and total distance traveled from t = 0 to t = 10 s? **(conceptual)**
9. A rocket sled accelerates from rest at 12 m/s² for 5.0 s, then coasts (no acceleration) for 3.0 s, and finally brakes at -8.0 m/s² until it stops. What is the maximum speed reached, and what is the total distance traveled? **(multi-step)**
10. An elevator starts from rest and accelerates upward at 1.5 m/s² until it reaches a speed of 6.0 m/s. It then travels at constant speed for 8.0 s before decelerating at 2.0 m/s² to a stop. What is the total height gained by the elevator? **(multi-step)**

### Kinematics 2D
1. A ball is kicked horizontally off the edge of a cliff at 15 m/s. The cliff is 80 m high. How far from the base of the cliff does the ball land? Use g = 9.8 m/s². **(numerical)**
2. A football is kicked at an angle of 37 degrees above the horizontal with an initial speed of 20 m/s. Find (a) the maximum height, (b) the time of flight, and (c) the horizontal range. Use g = 10 m/s². **(numerical)**
3. A cannon fires a shell at 45 degrees above the horizontal from the top of a 100 m cliff with an initial speed of 50 m/s. How far from the base of the cliff does the shell land? Use g = 9.8 m/s². **(multi-step)**
4. A boat can travel at 5.0 m/s in still water. It aims to cross a river that is 80 m wide and has a current of 3.0 m/s. If the boat heads directly across the river, (a) how long does it take to cross? (b) How far downstream does it end up? **(numerical)**
5. A projectile is launched from the ground at 30 degrees with a speed of 40 m/s. At what two times is the projectile at a height of 15 m? Use g = 10 m/s². **(numerical)**
6. Show that for a projectile launched on level ground, the maximum range is achieved at a launch angle of 45 degrees, and that the maximum range is v₀²/g. **(conceptual)**
7. A basketball player shoots from 7.0 m away from the basket. The ball leaves the player's hand at a height of 2.0 m and must enter the basket at a height of 3.05 m. If the ball is launched at 50 degrees above the horizontal, what initial speed is needed? Use g = 9.8 m/s². **(multi-step)**
8. A monkey hangs from a tree branch at a height of 12 m. A zookeeper standing 15 m away horizontally aims a tranquilizer dart directly at the monkey and fires at 25 m/s. The monkey drops from the branch at the instant the dart is fired. Does the dart hit the monkey? If so, at what height? Use g = 9.8 m/s². **(conceptual)**
9. Two projectiles are launched simultaneously from the same point. Projectile A is launched at 60 degrees with speed 30 m/s, and Projectile B at 30 degrees with speed 30 m/s. What is the distance between them at t = 2.0 s? Use g = 10 m/s². **(multi-step)**
10. A car travels around a circular track of radius 200 m at a constant speed of 25 m/s. What is the magnitude of the car's centripetal acceleration? How long does it take to complete one lap? **(numerical)**