Two forces, 1 = (3.90î − 2.60ĵ) N and 2 = (3.65î − 8.05ĵ) N, act on a particle of mass 2.10 kg that is initially at rest at coordinates (+1.60 m, +3.50 m).   (a) What are the components of the particle's velocity at t = 11.8 s?  = 42.362i−59.826j m/s (b) In what direction is the particle moving at t = 11.8 s? 305.302 ° counterclockwise from the +x-axis (c) What displacement does the particle undergo during the first 11.8 s? Δ = ????? m

A child riding a bicycle has a total mass of 30.6 kg. The child approaches the top of a hill that is 27.9 m high 27.9 and is 86.8 m (ℓ)  long at 12.1 m/s. If the force of friction between the bicycle and the hill is 26.7 N, what is the child's velocity at the bottom of the hill? (Disregard air resistance, g = 9.8 m/s2.)

Two students are pushing crates across a frictionless floor. The crates are initially at rest. Bing applies a horizontal force of 13 N to his crate. Bob, who is taller than Bing, pushes on his crate at an angle of 53 degrees below the horizontal, also with a force of 13 N. Find the ratio of the masses of the two crates if Bing's crate is moving at twice the speed of Bob's crate after they have traveled a distance of 23.5 m across the floor?

k A 13.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by = 10t² + 1tj where is in meters per second and t is in seconds. (Use the following as necessary: t.) V (a) Find its position as a function of time. ŕ= esc 10/³1 + ²/2 2²; 3 (b) Describe its motion qualitatively. The particle starts from rest at the origin, starts moving in the y direction, and gains speed faster and faster while turning to move more and more nearly parallel to the x axis. Score: 0.06 out of 0.06 Comment: (c) Find its acceleration as a function of time. a = 20ti + lj m/s² (d) Find the net force exerted on the particle as a function of time. F= T= (e) Find the net torque about the origin exerted on the particle as a function of time. N m X X (f) Find the angular momentum of the particle as a function of time. Ľ Need Help? Read It F1 N x (g) Find the kinetic energy of the particle as a function of time. K= x kg m²/s X (h) Find the power injected into the particle as a…

Besides the gravitational force, a 2.90-kg object is subjected to one other constant force. The object starts from rest and in 1.20 s experiences a displacement of (4.30î − 3.30ĵ) m, where the direction of ĵ is the upward vertical direction. Determine the other force. (Express your answer in vector form.)

A constant applied force of 46.0 N lifts an 2.50 kg mass straight up resulting in a final speed of 4.8 m/s. what distance did the mass move if it was initially at rest?

A freight train consists of two 8.00×104 kg5.60×104 kg engines and 45 cars with average masses of 5.50×104 kg5.50×104 kg. (a) What force must each engine exert backward on the track to accelerate the train at a rate of 4.00×10−2 m/s if the force of friction is 6.20×105 N, assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

A bowling ball weighing 46.5 N initially moves at a speed of 5.10 m/s. How long must a force of 44.5 N be applied to the ball to stop it?

(Assume no friction forces) A train of 100 railroad cars each with a mass of 6 x 104 kg is being pulled by a locomotive that has a mass of 4.5 x 105 kg.  The train leaves the freight yard at 12:00 noon on May the 5th.  It starts from an initial velocity of 0.  It takes the locomotive 8 kilometers to get the train up to a speed of 75 km/hr.  The train then travels at an average speed of 75 km/hr for 4,200 km.  After 4,200 km the train decelerates to a stop in 20 minutes.  How long in minutes (to the nearest hundredth of a minute) did it take to reach 75 km/hr at the beginning?  How much work was done to get the train to 75 km/hr.  What was the KE of the train when it reached 75 km/hr?  How much work was done on the train during the time it traveled the 4,200 km at 75 km/hr?  What is the total distance the train traveled from beginning to end to the nearest km?  What date and time does it arrive at its destination? (Date: Hour: min)? What is the work required to stop the train? What was…