A proton of mass 1.6726 × 10^-27 kg and a deuteron of mass 3.34364 × 10^-27 kg have the same amount of kinetic energy. Find the speed of the proton (v_p) in terms of the speed of the deuteron (v_d).

Is it realistic to assume that a sprinter of mass 70 kg could run fast to have a kinetic energy of 2600 J?

A loaded heavy construction vehicle has a mass of 9850 kg. The power output of the engine is 420 hp. The engine and transmission dissipate 15% of the power output, delivering 85 % to the wheels. Suppose 80% of the vehicle's weight is carried by the drive wheels; determine the greatest acceleration of the vehicle on a tarmac road when μ_s = 1.2.

A pick-up truck's engine delivers a maximum power of 120 hp. The truck is loaded to a total mass of 2250 kg. Inefficiencies in the engine and transmission dissipate 20% of the generated power while 80% is successfully delivered to the drive wheels. The truck's mass is distributed, so the drive wheels carry 3/5 of the total mass. When the truck accelerates at maximum acceleration (µ_s = 0.90), determine the speed attained at maximum power output. Hint: draw a free-body diagram of the truck.

A box is subjected to a 2D force, F = (xy² i + 3xyj) N, which depends on the x and y positions. The x and y coordinates are measured in m. The box starts at the origin and moves straight to (0,m). The box takes a right-angled turn and moves straight to (n,m). Determine the work done by the force.

A boulder experiences 2D forces that vary with position according to F = [xy i + (1/2)x² j] N. The positions x, and y are in m. State (with reason) if the force is conservative.

Spacecrafts, P and Q, have been deployed to orbit around the center of the Earth. Spacecraft P is moving at an altitude of 5.50$\times$10³ km, while spacecraft Q is at an altitude of 10.8$\times$10³ km. Determine the kinetic energies of P and Q, if their mass is 2.00$\times$10³ kg each. Assume the orbits are circular.

Hint: gravitational constant G = 6.67$\times$10^-11 Nm²/kg², mass of earth M_E = 5.98$\times$10²⁴ kg, radius of earth = 6.38$\times$10⁶ m