Newton's 2nd & 3rd Law

When a rock is propelled along a straight line in deep space by a constant force, its acceleration is directly proportional to the force acting on it. Therefore, if the force on the rock decreases by half, its acceleration will also decrease by half. This is because the force and acceleration have a linear relationship, meaning that any change in force will result in an equal change in acceleration.

When a softball player hits a ball with a bat, the action force is the impact of the bat against the ball. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the reaction force to the action force of the bat against the ball is the force of the ball against the bat.

The wagon's acceleration can be calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the force applied by the girl is 30N and the mass of the wagon is 10kg. By rearranging the formula, we can solve for acceleration: acceleration = force / mass. Substituting the given values, we get acceleration = 30N / 10kg = 3 m/s^2. Therefore, the correct answer is 3.

The force of friction between the block and the surface is equal to the applied force of 6N. This is because the block is being dragged without acceleration, which means that the force of friction is equal to the applied force in order to maintain a constant velocity.

The bullet's acceleration is more than the gun's acceleration because it has less mass. According to Newton's second law of motion, the acceleration of an object is inversely proportional to its mass when the force acting on it is constant. Since the bullet has less mass compared to the gun, it experiences a greater acceleration when the same force is applied to both objects.

To equally accelerate a 10kg brick, one would have to push with 10 times as much force. This is because according to Newton's second law of motion, force is directly proportional to the mass and acceleration of an object. Since the mass of the 10kg brick is 10 times greater than the 1kg brick, the force required to accelerate it would also need to be 10 times greater. Therefore, pushing with 10 times as much force would result in equal acceleration for the 10kg brick.

Terminal velocity occurs when the net force on a falling object is zero, meaning that the gravitational force pulling it downward is balanced by the air resistance pushing upward. At this point, the object no longer accelerates during free fall and reaches a constant speed. Additionally, the air resistance on the object is equal to its weight, further contributing to the balance of forces. Therefore, all of the statements mentioned are correct explanations for terminal velocity.

The lead-filled ball will reach the ground first because it has a greater mass compared to the regular ball. According to Newton's second law of motion, the acceleration of an object is inversely proportional to its mass when the force acting on it is constant. Since both balls experience the same gravitational force, the lead-filled ball will have a smaller acceleration due to its larger mass. As a result, it will take longer for the lead-filled ball to decelerate and reach the ground compared to the regular ball.

The correct answer is surface area and speed. When an object falls through the air, the larger its surface area, the more air resistance it experiences. This is because a larger surface area creates more contact with the air molecules, leading to a greater force opposing the object's motion. Similarly, the speed of the falling object also affects air resistance. As the speed increases, the air resistance also increases, as more air molecules collide with the object per unit of time. Therefore, both surface area and speed play a significant role in determining the amount of air resistance experienced by a falling object.

The light woman will get to a state of zero acceleration first. This is because her lighter weight allows her to experience less air resistance compared to the heavy man. As a result, she will reach a state of zero acceleration faster than the heavy man.

If the acceleration of an object doubled while the force applied to the object quadrupled, according to Newton's second law of motion (F = ma), the mass of the object must have doubled as well. This is because when the force applied to an object increases, the object's mass also needs to increase in order to maintain the same acceleration.

The heavier person slides a distance of 4m because the force exerted by each person in a tug-of-war is proportional to their mass. Since the heavier person is twice as massive as the other person, they exert twice the force. Since the rope is frictionless, the force exerted by the heavier person causes them to slide a greater distance than the lighter person. Therefore, the heavier person slides a distance of 4m.

When a bug splatters on a windshield, the force exerted by the car on the bug is greater than the force exerted by the bug on the car. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, the action is the force exerted by the car on the bug, and the reaction is the force exerted by the bug on the car. Therefore, the force of the bug on the car is less and in the opposite direction.

The bug has the greater acceleration because it is able to accelerate faster than the car. This means that the bug can increase its velocity at a quicker rate compared to the car.

As the skydiver falls, the air resistance acting against her motion increases. This air resistance creates a force that opposes her downward motion, causing a decrease in her acceleration. This means that as her velocity of fall increases, her acceleration decreases.

The stopping force acting on the block can be determined using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the block has a mass of 5kg and comes to rest in 2 seconds. To calculate the acceleration, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation, we get a = (v - u) / t. Since the block comes to rest, the final velocity is 0. Plugging in the values, we have a = (0 - 10) / 2 = -5 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity. Finally, we can calculate the stopping force using the formula F = ma, where F is the force, m is the mass, and a is the acceleration. Thus, F = 5kg * -5 m/s^2 = -25N. The negative sign indicates that the force is acting in the opposite direction of the initial velocity. However, since the question asks for the magnitude of the force, we take the absolute value, resulting in a force of 25N.