Newton's first law of motion and its mathematical problems with solutions

 Newton's first law of motion, also known as the law of inertia, states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Here are 10 mathematical problems along with their solutions based on this law:

1. Problem: A car is traveling along a straight road at a constant speed of 20 m/s. What is the net force acting on the car?

   • Solution: Since the car is moving at a constant speed, there is no change in velocity, and according to Newton's first law, the net force acting on the car is zero.

2. Problem: A block rests on a frictionless surface. Determine the net force acting on the block.

   • Solution: The block is at rest, so its velocity is constant, and according to Newton's first law, the net force acting on the block is zero.

3. Problem: An object is moving with a velocity of 10 m/s to the right. What is the net force acting on the object?

   • Solution: If the object is moving with constant velocity, there is no acceleration, and thus, according to Newton's first law, the net force acting on the object is zero.

4. Problem: A spacecraft is traveling through space with a constant velocity. Determine the net force acting on the spacecraft.

   • Solution: Since the spacecraft is traveling with constant velocity, there is no change in its motion, and according to Newton's first law, the net force acting on the spacecraft is zero.

5. Problem: A ball is rolling across a level surface without slowing down. Analyze the net force acting on the ball.

   • Solution: If the ball is rolling without any change in its motion, there is no net force acting on it according to Newton's first law.

6. Problem: A feather falls through the air at a constant velocity. Calculate the net force acting on the feather.

   • Solution: If the feather is falling at a constant velocity, there is no acceleration, and thus, according to Newton's first law, the net force acting on the feather is zero.

7. Problem: A book slides across a table at a constant speed. Determine the net force acting on the book.

   • Solution: Since the book is moving with constant speed, there is no acceleration, and according to Newton's first law, the net force acting on the book is zero.

8. Problem: An ice skater glides across the ice with constant velocity. Analyze the net force acting on the skater.

   • Solution: If the skater is moving with constant velocity, there is no acceleration, and thus, according to Newton's first law, the net force acting on the skater is zero.

9. Problem: A planet orbits around the Sun in a stable orbit. Describe the net force acting on the planet.

   • Solution: In a stable orbit, the gravitational force between the planet and the Sun provides the necessary centripetal force, and according to Newton's first law, the net force acting on the planet is zero.

10. Problem: A ball is thrown straight up into the air. What is the net force acting on the ball at the highest point of its trajectory?

    • Solution: At the highest point of its trajectory, the ball momentarily comes to rest before falling back down due to gravity. Therefore, the net force acting on the ball at that point is zero according to Newton's first law.

These problems illustrate various scenarios where objects remain at rest or move with constant velocity, in accordance with Newton's first law of motion.