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Differential Calculus Week

For this week, we are going to post differential calculus problem - one problem everyday.

Challenge your calculus skills by answering these questions.

A car moving at 10.0 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seat belt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70.0 kg....

College Physics Chapter 8 Problem 8 A car moving at 10.0 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seat belt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70.0 kg.

A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600.0 m/s in a time of 2.00 ms (milliseconds)?

College Physics Chapter 8 Problem 7 A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600.0 …

The mass of Earth is 5.972e24 kg and its orbital radius is an average of 1.496e11m. Calculate its linear momentum.

The linear momentum of earth given its mass and orbital radius The mass of Earth is 5.972e24 kg and its orbital radius is an average of 1.496e11m. Calculate its linear momentum.

A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. Compute the time required for a force of 1500 N to bring the car to rest.

College Physics by Openstax Chapter 8 Problem 5 A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. Compute the time required for a force of 1500 N to bring the car to rest.

(a) What is the momentum of a garbage truck that is 1.20×104 kg and is moving at 30.0 m/s? (b) At what speed would an 8.00-kg trash can have the same momentum as the truck?

College Physics by Openstax Chapter 8 Problem 4 (a) What is the momentum of a garbage truck that is 1.20×104 kg and is moving at 30.0 m/s? (b) At what speed would an 8.00-kg trash can have the same momentum as the truck?

(a) At what speed would a 2.00×104-kg airplane have to fly to have a momentum of 1.60×109 kg⋅m/s (the same as the ship’s momentum in the problem above)? (b) What is the plane’s momentum when it is taking off at a speed of 60.0 m/s?

College Physics by Openstax Chapter 8 Problem 3 (a) At what speed would a 2.00×104-kg airplane have to fly to have a momentum of 1.60×109 kg⋅m/s (the same as the ship’s momentum in the problem above)? (b) What is the plane’s momentum when it is taking off at a speed of 60.0 m/s?