A ball is shot from a compressed-air gun at twice its terminal speed. What is the ball's initial acceleration, as a multiple of g, if it is shot straight up?

Astronauts in space 'weigh' themselves by oscillating on a spring. Suppose the position of an oscillating 75 kg astronaut is given by $x=\left(0.30\text{m}\right)\sin \left(\right(\pi \text{rad/s})\times t)$, where t is in s. What force does the spring exert on the astronaut at (a) t = 1.0 s and (b) 1.5 s? Note that the angle of the sine function is in radians.

A 500 g ball moves horizontally with velocity v_𝓍 = ( 15 m) / (t + 1 s) for t > 0 s. What is the net force on the ball at t = 1 s?

What is the magnitude of the acceleration of a skydiver at the instant she is falling at one-half her terminal speed?

A particle of mass m moving along the x-axis experiences the net force Fₓ = ct, where c is a constant. The particle has velocity v₀ₓ at t = 0. Find an algebraic expression for the particle's velocity vₓ at a later time t.

A block of mass m is at rest at the origin at t = 0. It is pushed with constant force F₀ from 𝓍 = 0 to 𝓍 = L across a horizontal surface whose coefficient of kinetic friction is μₖ = μ₀ ( 1 - 𝓍/L ) . That is, the coefficient of friction decreases from μ₀ at 𝓍 = 0 to zero at 𝓍 = L. b. Find an expression for the block's speed as it reaches position L.

A spherical particle of mass m is shot horizontally with initial speed v₀ into a viscous fluid. Use Stokes' law to find an expression for vₓ (t), the horizontal velocity as a function of time. Vertical motion due to gravity can be ignored.