Final answer:
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In a head-on collision between two vehicles, if they lock together after impact, their combined velocity can be calculated using the law of conservation of momentum. In this scenario, the combined velocity of the two vehicles will be 0.4 m/s.
Step-by-step explanation:
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In a collision, the total momentum before the collision is equal to the total momentum after the collision.
In this scenario, we have two vehicles colliding head-on. The first vehicle has a mass of 2 tonnes and a velocity of 4 m/s, while the second vehicle has a mass of 3 tonnes and a velocity of -2 m/s. If the two vehicles lock together after the impact, the combined mass of the two vehicles is 5 tonnes. To find the combined velocity, we can use the law of conservation of momentum.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Initial momentum = Final momentum
(mass of first vehicle * velocity of first vehicle) + (mass of second vehicle * velocity of second vehicle) = (total mass of the two vehicles * combined velocity)
(2 tonnes * 4 m/s) + (3 tonnes * -2 m/s) = (5 tonnes * combined velocity)
8 tonnes m/s - 6 tonnes m/s = 5 tonnes * combined velocity
2 tonnes m/s = 5 tonnes * combined velocity
combined velocity = 2 tonnes m/s / 5 tonnes
combined velocity = 0.4 m/s