To solve this problem, we can use 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.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Let's denote the initial velocity of the car as v1, the initial velocity of the truck as v2 (which is 0 since it is stationary), and the final velocity of both the car and the truck after the collision as vf.
According to the conservation of momentum:
Initial momentum of the car + Initial momentum of the truck = Final momentum of the car and truck
(mass of the car × initial velocity of the car) + (mass of the truck × initial velocity of the truck) = (mass of the car + mass of the truck) × final velocity of the car and truck
(1000 kg × 25 m/s) + (1500 kg × 0 m/s) = (1000 kg + 1500 kg) × vf
25000 kg·m/s = 2500 kg × vf
Now, we can solve for vf:
vf = 25000 kg·m/s / 2500 kg = 10 m/s
Therefore, the velocity of the truck after the collision is 10 m/s. Both the car and the truck move together with this velocity.