91Ó°ÊÓ

Collision physics deals with the interactions between bodies that come into contact with each other. When two vehicles collide, like the car and SUV in our exercise, they exert forces on each other over a short time period.
This results in a quick transfer of momentum. Momentum is essentially the quantity of motion an object possesses and is calculated by combining the mass and velocity of the object.
One of the fascinating aspects of collision physics is the concept of conserving quantities, such as momentum. We often assume that in the absence of external forces, the total momentum of a system remains constant before and after the collision.
This assumption allows us to use the principle known as the conservation of momentum to analyze and predict the outcomes of collisions. In this particular exercise, due to the nature of the head-on collision and both vehicles coming to a stop, the total pre-collision momentum was zero. This is a key clue in resolving the problem.

The momentum equation is critical to solving collision problems. This equation stems from the conservation of momentum principle, which states that the total momentum before a collision equals the total momentum after the collision, assuming no external forces are involved.
For our problem, the comprehensive equation is expressed like this: \[ m_1 \cdot v_1 + m_2 \cdot v_2 = 0 \]Where

• \(m_1\) is the mass of the first vehicle (car),
• \(v_1\) is the velocity of the first vehicle before the collision,
• \(m_2\) is the mass of the second vehicle (SUV),
• \(v_2\) is the velocity of the second vehicle before the collision (which we are solving for).

Since the car's momentum is positive and the SUV's negative due to opposite directions, the equation balances the momenta out to zero. Through rearranging the equation, you can find the needed velocity of the SUV.

To calculate the SUV's speed right before the collision, it's time to solve the momentum equation provided. You know the mass of the car is 1100 kg and it moves at 32 m/s. Hence its momentum is calculated as follows:\[1100 \times 32 = 35200 \, \text{kg} \cdot \text{m/s}\]
Now, suppose the total momentum is zero; hence the SUV's momentum must negate the car's:\[2500 \times (-v_{\text{SUV}}) = -35200 \, \text{kg} \cdot \text{m/s}\]
The steps to derive the SUV's speed are simple:

• Rearrange the equation to solve for \(v_{\text{SUV}}\):\[v_{\text{SUV}} = \frac{35200}{2500}\]
• Perform the division to find \(v_{\text{SUV}}\):\[v_{\text{SUV}} = 14.08 \, \text{m/s}\]

Thus, the SUV was traveling at approximately 14.08 m/s. This calculation not only demonstrates the power of using the momentum equation but shows how physical concepts translate into real-world speed determinations.