To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the velocity of the car after the collision as v_car and the velocity of the truck after the collision as v_truck.
Before the collision: Momentum of the car = mass of the car * velocity of the car = 1000 kg * 25 m/s = 25000 kg·m/s Momentum of the truck = mass of the truck * velocity of the truck = 1500 kg * 0 m/s = 0 kg·m/s
After the collision, the car and truck move together, so their combined momentum is: Momentum of the car and truck = (mass of the car + mass of the truck) * velocity of the car and truck
We can set up the equation based on the conservation of momentum:
25000 kg·m/s + 0 kg·m/s = (1000 kg + 1500 kg) * v_car_and_truck
Simplifying the equation:
25000 kg·m/s = 2500 kg * v_car_and_truck
Dividing both sides by 2500 kg:
v_car_and_truck = 25000 kg·m/s / 2500 kg
v_car_and_truck = 10 m/s
Therefore, the velocity of the car and truck together after the collision is 10 m/s.