91Ó°ÊÓ

Momentum is a fundamental concept in physics, rooted in the conservation of energy and motion. It describes the quantity of motion an object possesses and is dependent on both mass and velocity.
In formula terms, it is expressed as:

• P = m × v

where P is the momentum, m is mass, and v is velocity.
Calculating the momentum of an object involves these variables and gives a sense of how hard it might be to stop an object in motion. This directs us to understanding the behavior of bodies in collisions and how their motions will result in a transfer of momentum. In a collision scenario like the one provided, each object's momentum before the collision sums up to the total system momentum. In our exercise, the car's significant mass and velocity imply it carries a considerable momentum of 35200 kg·m/s.

Head-on collisions are a specific type of contact scenario where two objects collide while moving directly toward one another. In such cases, each object's momentum contributes to the system's total momentum.
During these events, the key principle is that the total momentum in the system remains conserved if no external forces intervene. That means the combined momentum of the car and the SUV before the collision equals the momentum after the collision.
In our exercise, both vehicles come to a halt, indicating their combined momentum is zero post-collision, meaning their pre-collision momenta must perfectly balance one another to satisfy the conservation principle.
This balance means:

• The car's forward momentum would be equal in magnitude but opposite in direction to the SUV's backward momentum.

Such insights highlight how predictably and neatly physics governs collisions.

Determining the velocity of an object in a collision, especially in head-on ones, involves leveraging the conservation of momentum.
In our scenario, the problem states that the combined momentum of both the car and the SUV post-collision is zero. This directly allows us to calculate the unknown velocity of the SUV using:

• Conservation Equation: The momentum from the car is cancelled by the momentum from the SUV.
• \[ -2500 \, \text{kg} \times v_2 = -35200 \, \text{kg} \cdot \text{m/s} \]

Solving this equation involves isolating the unknown velocity variable \(v_2\) on one side of the equation:

• \[ v_2 = \frac{-35200}{-2500} = 14.08 \, \text{m/s} \]

This solution reveals the speed at which the SUV must have been traveling; the negative sign was addressed earlier, indicating the SUV moved in the opposite direction of the car's motion pre-collision.