A 1500 kg car traveling 5.0 m/s colldies head on with 3000 kg truck traveling 7.0 m/s in the opposite direction. If the bumpers lock (the collision is inelastic), a) what is the velocity of the two vehicles together immediately following the collision?
b) what is the magnitude of the change in velocity experienced by the driver of each car during the collision?

a) v₃ = - 3 [m/s] The negative sign means that both vehicles will move to the left.

b) see the explanation below

Explanation:

To solve this problem we must use the principle of conservation of linear momentum, which tells us that momentum is preserved before and after a collision.

Let's take the car's movement to the right as positive and truck movement to the left as negative, the momentum before the collision is written to the left of the equal sign, the momentum after the collision will be taken after the equal sign.

ΣMbefore = ΣMafter

M = m*v [kg*m/s]

(m₁*v₁) - (m₂*v₂) = (m₁+m₂)*v₃

where:

m₁ = mass of the car = 1500 [kg]

v₁ = velocity of the car = 5 [m/s]

m₂ = mass of the truck = 3000 [kg]

v₂ =  velocity of the truck = 7 [m/s]

v₃ = final velocity [m/s]

(1500*5) - (3000*7) = (1500+3000)*v₃

v₃ = - 3 [m/s]

b)

To be able to solve the velocities we must perform the arithmetic operations of sums of velocities taking into account the sign of each one.

for the car

Vc = 5 - 3 = 2 [m/s] At the time of the crash the car experiences a speed reduction of 2 [ m/s]

for the truck

Vt = 7 - 3 = 4 [m/s] At the time of the crash the truck experiences a speed reduction of 4 [ m/s]

unlike poles attract