A car (mass = 1080 kg) is traveling at 25.4 m/s when it collides head-on with a sport utility vehicle (mass = 2750 kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. At what speed was the sport utility vehicle traveling?

Since the 2 vehicles came to a halt,their momentums were equal.

m1*Vi = m2*V2.
1080*25.4 = 2750*V2.
Solve for V2.

To find the final velocity (v2) of the sport utility vehicle (SUV), we can use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.

The formula to calculate momentum is:
Momentum = mass × velocity

Since the mass of the car (m1) is given as 1080 kg and its velocity (v1) is 25.4 m/s, we can calculate its momentum before the collision:
Momentum1 = m1 × v1

For the SUV, let's assume its velocity is v2 after the collision. Its mass (m2) is given as 2750 kg, so we can calculate its momentum before the collision:
Momentum2 = m2 × v2

According to the conservation of momentum, the sum of the initial momenta is equal to the sum of the final momenta:
Momentum1 + Momentum2 = 0

Substituting the known values:
(m1 × v1) + (m2 × v2) = 0

Now, let's plug in the values:
(1080 kg × 25.4 m/s) + (2750 kg × v2) = 0

Simplifying the equation further:
27432 kg·m/s + 2750 kg·v2 = 0

Rearranging the equation to solve for v2:
2750 kg·v2 = -27432 kg·m/s
v2 = -27432 kg·m/s ÷ 2750 kg

Calculating the value of v2:
v2 ≈ -9.97 m/s

The negative sign indicates that the SUV was traveling in the opposite direction, as assumed. Therefore, the sport utility vehicle was traveling at approximately 9.97 m/s in the opposite direction.