A 4 kg particle has a position vector as a function of time given by: r(t) = 3 t3i + -6 t3j  (m) This particle has a single force acting on it.  Calculate the power output of this force t = 1 s into the particle's journey, in W. (Please answer to the fourth decimal place - i.e 14.3225)

A mechanic pushes a 2480-kg car from rest to a speed of ?v, doing 4.66e3 J of work in the process. During this time, the car moves 25.7 m. (Neglect the friction between car and road.) (a) Find ?v.  m/s ( ± 0.02 m/s) (b) Determine the horizontal force exerted on the car.  N ( ± 2 N)

A 5 kg block slides down a 9 m long incline that makes an angle of 55 degrees with the horizontal.  The coefficient of kinetic friction between block and incline is 0.49.  Calculate the work done by friction as the block slides. (Please answer to the fourth decimal place - i.e 14.3225)

A young woman on a skateboard is pulled by a rope attached to a bicycle. The velocity of the skateboarder is v⃗ → = (5.1 m/sm/s )x^ and the force exerted on her by the rope is F⃗ → = (17 NN)x^+ (12 NN)y^. Find the work done on the skateboarder by the rope in 20 seconds.

A body of mass 1.68 kg is at rest and subjected to a force of 11.91 N. Find the kinetic energy at the end of 4 s. No unit is required for the final answer.

A mechanic pushes a 3850 kg car from rest to a speed of v, doing 5083 J of work in the process. Find the speed v. Neglect friction between car and road. Answer in units of m/s.

A 12.0 kg box is given an initial push that starts it sliding across the floor. It eventually comes to a stop. If the box has an initial velocity of 3.5 m/s, how much work is done by friction to cause it to come to a stop? (Yes, you are correct, you do not know the coefficient of friction.)

Strictly don't use chatgpt. I need a handwritten solution only

The figure here shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F₁ = 2.60 N, F₂= 3.60 N, and F3 = 10.0 N, and the indicated angles are 02 = 49.0° and 93 = 30.0°. What is the net work done on the canister by the three forces during the first 3.90 m of displacement? 8₂ 03 Number i 11 Unit J

A golfer hit a 44.84 gram golf ball from the fairway giving it an initial velocity of 38.6 m/s.  It lands on the green, which is at the same elevation as the fairway, and strikes the ground with a final velocity of 15.2 m/s.  What is the work (in J) done on the ball by the non-conservative friction forces [round your final answer to one decimal place]?