Work, Energy & Power

A variable force F = (4x + 1) N acts on a body. Find the work done as it moves from x = 0 to x = 2 m.

A 2 kg block is dropped from 0.3 m above a vertical spring (k = 500 N/m). Find the maximum compression. (g = 10 m/s²)

A force F = 5t (N) acts on a particle moving with velocity v = 4t (m/s), both along the same line. Find the total work done from t = 0 to t = 3 s.

The potential energy of a particle is U = x³ − 3x (in joules). Find the position(s) of equilibrium.

A 4 kg block slides 8 m down a rough 37° incline (μ = 0.25), starting from rest. Find its speed at the bottom. (sin37°≈0.6, cos37°≈0.8, g=10 m/s²)

A 1 kg block compresses a spring (k = 250 N/m) by 0.2 m against friction (μ = 0.25) and is released. Find its speed as the spring reaches natural length. (g = 10 m/s²)

A force of 20 N acts on a body at 37° to its displacement of 10 m. Find the work done. (cos37°≈0.8)

A 4 kg body, initially at rest, has 72 J of work done on it (no friction). Find its final speed.

A spring with k = 600 N/m is compressed by 0.2 m. Find the elastic PE stored.

A force of 80 N moves an object at a constant velocity of 3 m/s in its own direction. Find the power delivered.

A machine has an input power of 2000 W and a useful output of 1500 W. Find its efficiency.

The work done on a particle is W = 6t³ (joules, t in seconds). Find the instantaneous power at t = 2 s.