# Accelerating Car

Pro Problems > Physics > Motion and Forces > Linear Motion > Force## Accelerating Car

## Solution

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### Fastest Ride

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?

### Tractor on a Flatbed

A 6000 kg tractor rests on a flatbed, held in place by chains. The chains provide a maximum horizontal force of 8000 N. When the flatbed is traveling 20 m/s, what is the minimum stopping distance if the chains are not to break?

### Out of Control Elevator

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?

### Cart with Groceries

1.A horizontal force of 10N is applied to a 30 kg cart on a level floor.

- How far will it move in 3.0s, starting from rest? Ignore friction.
- How far will it move in 3.0s if 30N of groceries is added to the cart first?

### Car with Passengers

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?

### Howard doesn't Move

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.

### Force on Two Objects

If a force accelerates 4.5 kg at 40 m/s^{2}, that same force would accelerate 18 kg by how much?

### Luke Skywalker's X-Wing

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?

### Force and Friction on a Crate

If the coefficient of kinetic friction between a 35 kg crate and the floor is .30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if µ_{k} is zero?

### Car and Motorcycle

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?