Howard is standing in the middle of a skating rink (we'll assume no friction), and his four friends Alice, Bernie, Christopher, and David approach him from each of the four compass directions - north, east, south, and west, respectively.

Alice pushes on Howard with a force of x + 20 Newtons. Bernie pushes on him with a force of 2x + y Newtons. Christopher pushes on him with a force of 2x - y Newtons, and David pushes with a force of 5y Newtons.

Howard, though being pushed from all directions, does not move. Calculate the forces being applied in all four directions.

I would like to get from City A to City B, which are 200 miles apart, in the shortest amount of time, given the stipulation that I don't want to experience a force more than 4 times the force of gravity. What is shortest amount of time this trip can take?

A car accelerates from 10 m/s to 50 m/s while traveling 400 m. The mass of the car is 1500 kg. What force was applied to the car?

Four passengers with mass 85 kg apiece are added to the problem above, how much would that change the force required?

A 50 kg sled starts at rest, and is being pushed across a horizontal frictionless surface with a force of 30 N. The wind is pushing against the sled. The sled travels 100 meters while accelerating to 10 m/s. What is the force of the wind on the sled?

A 50 slug car can accelerate from 0 to 50 ft/s while traveling 1000 feet. The car then stops, and a passenger gets in. Now the car can accelerate from 0 to 50 ft/s while traveling 1050 feet. What is the weight of the passenger?

A force is applied to a 1000 kg car, and causes the car to accelerate from 0 m/s to 25 m/s while traveling 200 m. The same force is applied to a 600kg motorcycle.  How far will the motorcycle travel while accelerating from 10 m/s to 40 m/s?

After Luke Skywalker got his X-Wing fighter out of the swamp on Dagobah, he wanted to make it fly. The mass of the ship is 5,000 kg. Luke applies (using the force) an upward force of x Newtons. Yoda, who doesn't want Luke to get too confident, applies a downward force which is two-thirds of Luke's force.

Luke's Skywalker X-Wing fighter lifts off to a height of 2 km in 5 seconds. How much force did Luke apply?

A hockey stick travels backward 11.0 cm while intercepting a 0.140 kg puck. How much force did the stick exert on the puck to bring the puck from 35.0 m/s to rest?

An elevator has a mass of 2,000 kg.  An upward force of 21,000 Newtons is applied to the elevator. The elevator travels up 50 floors, and each floor is 2.5 meters tall, with a 20 centimeter gap between floors. How long does it take the elevator to arrive, and at what speed will it be traveling?

Jamal is pulling a 4,900 N box with a force of 500 N. Jakob is pulling in the opposite direction with a force of 350 N. How fast will the box be moving after 5 seconds?