University Physics I: Mechanics

Use this for “x = 2t³ − 9t² + 12t + 4 (m, s). Find the velocity and acceleration at t = 3 s.”

Use this for “A ball is thrown from 2 m up at 20 m/s, 60° above level. Where is it 2.5 s later, and how fast and which way is it moving?”

Use this for “Blocks of 3 kg and 5 kg hang from the two ends of a string over a pulley. Find their acceleration and the string’s tension.”

Use this for “A 2 kg ball is dropped from rest, and the air pushes back with 4 kg/s times its speed. Find its terminal speed and how fast it falls after 1 s.”

Use this for “A curve of radius 80 m is banked at 12°. At what speed can a 1500 kg car take it with no friction, and how hard does the road push on it?”

Use this for “A force F = 0.5x³ N pushes a cart along a track from x = 2 m to x = 4 m. How much work does it do?”

Use this for “A particle has potential energy U(x) = 2x³ − 6x² (U in J, x in m). Find the force on it at x = 0.5 m, and where it can rest in stable equilibrium.”

Use this for “A 40 kg sled starts down a 50 m slope at 20° moving at 3 m/s, with μₖ = 0.08. How much heat does friction make, and how fast is the sled at the bottom?”

Use this for “A 0.5 kg puck sliding east at 3 m/s catches a 1.5 kg puck sliding east at 1 m/s, and they bounce apart elastically. What are their velocities after?”

Use this for “A light 1.2 m rod holds 0.4 kg at 0.1 m, 0.6 kg at 0.5 m and 1 kg at 1.1 m. Where is its center of mass?”

Use this for “A kick pushes a 0.43 kg ball at rest with a force that rises evenly to 2,400 N and falls back to 0 over 8 ms. What is the impulse, and how fast does the ball leave?”

Use this for “A 12,000 kg rocket burns fuel until it weighs 4,000 kg, its exhaust leaving at 3,000 m/s. How much speed does it gain?”

Use this for “A 2 kg rod 1.5 m long turns about an axis 0.5 m from its center. Find its moment of inertia about that axis.”

Use this for “A 3 kg bucket hangs from a rope wound round a 5 kg solid disk pulley of radius 0.2 m. Find the bucket’s acceleration, the rope’s tension and the pulley’s angular acceleration.”

Use this for “A skater spinning at 3 rad/s with her arms out (I = 5 kg·m²) pulls them in to I = 2 kg·m². Find her new spin and the work her arms do.”

Use this for “A 300 N ladder leans on a smooth wall at 65° to the floor. How hard does the wall push, and how rough must the floor be to hold it?”

Use this for “A 2 kg block on a 200 N/m spring has damping b = 1 kg/s and starts with a 0.1 m amplitude. Find ω′, Q and the amplitude after 4 s.”

Use this for “A 0.3 kg rod 1.2 m long swings from a pin at one end. Find its period and the length of a simple pendulum that keeps time with it.”

Use this for “Find the speed and period of a satellite 400 km above Earth.”

Use this for “How much potential energy does a 1000 kg satellite gain going from the ground to 400 km?”

Use this for “What fraction of an ice block (917 kg/m³) floats under seawater (1,025 kg/m³)?”

Use this for “Water stands 2 m above a 2 cm² hole in a tank. How fast does it leave, and at what flow rate?”

Use this for “A 0.2 kg aluminium block at 90 °C goes into 0.5 kg of water at 20 °C. Find the final temperature.”

Use this for “How much heat flows through a concrete wall 10 m² in area and 20 cm thick when inside and outside differ by 20 °C?”

Use this for “An engine runs between 500 K and 300 K and takes in 1000 J. At most how much work can it do?”

Use this for “Find the entropy change of 1 kg of water heated from 20 °C to 80 °C.”