A 5.00-kg particle starts from the origin at time zero. Its velocityasa functionoftimeisgivenbyv = (6t 2i+ 2t j) where v is in meters per second and t is in seconds. (a) Find its position vector r as a function of time (b) its acceleration as a function of time,(c) the net force exerted on the particle as a function of time,

An approximately spherical exoplanet in a faraway galaxy happens to have a mass that is only (3/5) times our Earth’s mass. Curiously enough, any object abandoned near its surface will fall with the same vertical acceleration as it would on our Earth (that is, the exoplanet's g is equal to our terrestrial g). (a) What must be the average radius of such an exoplanet for this strange coincidence to be true? (b) If you weighed 650 N on the Earth, how much would you weigh on this exoplanet? 1

Don't use chat gpt It Chatgpt means downvote

An 77.0 kg spacewalking astronaut pushes off a 650 kg satellite, exerting a 105 NN force for the 0.430 ss it takes him to straighten his arms. How far apart are the astronaut and the satellite 1.40 min after the push begins?

A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 5.40-kg puck has a velocity of 1.20l m/s at one instant. Elght seconds later, its velocity is (6.0oi+ 8.0) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force. 3375 (b) Find its magnitude. 527

A rocket of mass 10^5 kg is launched fromthe surface of the Earth. This is a sketch of the rocket as it’s still in Earth’s atmo-sphere. The rocket is undergoing an accel-eration of 3 m/s^2 upward. There is a forceexerted on the rocket from the thrust of itsengines labeled here as FEngine (you can useFE for short). The rocket is still close to theEarth’s surface, so it is subject to Earth’s gravity, and it is also subject to a substan-tial air resistance force. a. Draw a complete free body diagram of the rocket with all forces acting on it, clearlyindicating which direction each forces act.  b. What is the weight of the rocket, and what is the net force on the rocket? c. If the force the engine is exerting is FE = 1.8×10^6 N, what is the magnitude of the forceof air resistance? d. What is the work done by the engine as the rocket rises 150 m?