1. a 2000 kg SUV is moving at 25 m/s. What force is needed to bring it to a stop in 8 seconds?

2. A 20 kg child is sitting in a 15 kg wagon that is moving at 3 m/s. what is the total momentum in the system?

3. A 75 kg train car moving at 2.4 m/s collides with a second identical train car at rest. if they hook together when the collide, what is the final speed of the two?

4. a 4000 kg train car moving at 2.4 m/s. same question as 3.

5. a 6 kg bowling ball and a 4 kg bowling ball are rolled toward each other. the 6 kg ball is initially moving at 5.1 m/s and the 4 kg ball is moving in the opposite direction at 1.3 m/s. if the 6 kg ball slows to 1.5 m/s, what is the final speed of the 4 kg ball?

please help

me with these questions.

1. The force needed to bring the SUV to a stop in 8 seconds is 6,250 N.
2. The total momentum in the system is 60 kg m/s.
3. The final speed of the two train cars is 2.4 m/s.
4. The final speed of the two train cars is 1.2 m/s.
5. The final speed of the 4 kg ball is 3.8 m/s.

Sure, I'd be happy to help you with these physics problems step-by-step!

1. To find the force needed to bring the SUV to a stop, we can use the equation:
force = mass × acceleration

Since the SUV is coming to a stop, the final velocity is 0 m/s. Therefore, the acceleration can be calculated using the following equation:
acceleration = (final velocity - initial velocity) / time
acceleration = (0 - 25) m/s / 8 s

Plugging this value into the force equation:
force = (2000 kg) × [ (0 - 25) m/s / 8 s ]

Calculating the force:
force = 2000 kg × (-25/8) m/s²

The force required to bring the SUV to a stop is -6250 N.

2. The total momentum in the system can be calculated by adding the individual momenta of the child and the wagon.
Momentum = mass × velocity

Child's momentum = (20 kg) × (3 m/s)
Wagon's momentum = (15 kg) × (3 m/s)

Total momentum = Child's momentum + Wagon's momentum

Plugging in the values:
Total momentum = (20 kg × 3 m/s) + (15 kg × 3 m/s)

The total momentum in the system is 105 kg·m/s.

3. In this scenario, we can apply the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Momentum before collision = Momentum after collision

The momentum of the first train car before the collision is given by:
Momentum1 = mass1 × velocity1
Momentum1 = (75 kg) × (2.4 m/s)

The momentum of the second train car before the collision is 0 since it's at rest.

Momentum before collision = Momentum after collision

Since the two train cars hook together, their final speed is the same. Let's call it Vf.

The total mass of the two train cars combined is 2 × 75 kg = 150 kg.

Momentum after collision = (150 kg) × Vf

Plugging in the values:
Momentum1 = (150 kg) × Vf

Setting the two momenta equal to each other and solving for Vf:
(75 kg) × (2.4 m/s) = (150 kg) × Vf

Solving for Vf:
Vf = (75 kg × 2.4 m/s) / 150 kg

The final speed of the two train cars after hooking together is 1.2 m/s.

4. We can follow the same approach as in question 3, using the principles of conservation of momentum.

Momentum before collision = Momentum after collision

The momentum of the train car before the collision is given by:
Momentum = mass × velocity
Momentum = (4000 kg) × (2.4 m/s)

The momentum of the second train car before the collision is 0 since it is at rest.

Momentum before collision = Momentum after collision

Since the two train cars hook together, their final speed is the same. Let's call it Vf.

The total mass of the two train cars combined is 2 × 4000 kg = 8000 kg.

Momentum after collision = (8000 kg) × Vf

Plugging in the values:
(4000 kg) × (2.4 m/s) = (8000 kg) × Vf

Solving for Vf:
Vf = (4000 kg × 2.4 m/s) / 8000 kg

The final speed of the two train cars after hooking together is 1.2 m/s.

5. To solve this problem, we can apply the principle of conservation of momentum.

Momentum before collision = Momentum after collision

The momentum of the 6 kg bowling ball before the collision is given by:
Momentum1 = mass1 × velocity1
Momentum1 = (6 kg) × (5.1 m/s)

The momentum of the 4 kg bowling ball before the collision is given by:
Momentum2 = mass2 × velocity2
Momentum2 = (4 kg) × (-1.3 m/s) (opposite direction)

Momentum before collision = Momentum after collision

Let's denote the final velocities as Vf1 and Vf2 respectively.

The total momentum after the collision is given by:
Total momentum after collision = (6 kg) × Vf1 + (4 kg) × Vf2

Plugging in the values:
(6 kg) × (1.5 m/s) + (4 kg) × Vf2 = (6 kg) × Vf1 + (4 kg) × Vf2

Rearranging the equation:
(6 kg) × Vf1 = (6 kg) × (1.5 m/s) + (4 kg) × Vf2 - (4 kg) × Vf2

Simplifying the equation:
(6 kg) × Vf1 = (6 kg) × (1.5 m/s)

Solving for Vf1:
Vf1 = (6 kg × 1.5 m/s) / 6 kg

The final speed of the 6 kg bowling ball is 1.5 m/s.

Since the final velocity of the 6 kg ball is given, you can substitute this value back into the momentum equation to find the final velocity of the 4 kg ball.

Sure, I can help you with these questions. To find the answers, we will use the principles of Newton's laws of motion and conservation of momentum. Let's break down each question and explain how to get the answer:

1. To find the force needed to stop the SUV, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = m * a). Since the SUV is coming to a stop, the final velocity is 0 m/s. The acceleration can be calculated using the formula a = (final velocity - initial velocity) / time taken. Plugging in the values, we get a = (0 - 25) m/s / 8 s = -3.125 m/s^2 (negative sign indicates deceleration). Now, we can calculate the force (F = m * a) where mass (m) is 2000 kg and acceleration (a) is -3.125 m/s^2.

2. The total momentum of a system is the sum of the individual momenta of each object in the system. The momentum of an object is given by the formula p = m * v, where mass (m) is in kg and velocity (v) is in m/s. In this case, the 20 kg child and the 15 kg wagon are moving together, so you need to calculate the momentum of each individually and then add them together to get the total momentum of the system.

3. To find the final speed of two colliding objects that stick together after the collision, we can use the principle of conservation of momentum. According to conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. First, calculate the initial total momentum using the formula p = m * v, where mass (m) is in kg and velocity (v) is in m/s. Then, use the equation m₁v₁ + m₂v₂ = (m₁ + m₂)vf to find the final velocity (vf) of the two train cars together.

4. Same as question 3, but with different values for the masses and velocities.

5. To solve this problem, we can also use the principle of conservation of momentum. Calculate the initial momentum of the system, which is the sum of the individual momenta of the 6 kg and 4 kg bowling balls. Then, use the equation m₁v₁ + m₂v₂ = (m₁ + m₂)vf to find the final velocity (vf) of the 4 kg bowling ball.

I hope this helps! If you have any specific values or calculations you need assistance with, please let me know.