A 1000-kg car traveling at 25 m/s runs into the rear of a stopped car that has a mass of 1500 kg and they stick together. What is the speed of the cars after the collision?

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In a collision between vehicles, such as in this case, the moving vehicle will lose out on some momentum (product of mass and velocity of the object), while the stationary vehicle will gain some momentum. Using the conservation of momentum, the momentum remains conserved as the following equation:

m1v1 +...

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In a collision between vehicles, such as in this case, the moving vehicle will lose out on some momentum (product of mass and velocity of the object), while the stationary vehicle will gain some momentum. Using the conservation of momentum, the momentum remains conserved as the following equation:

m1v1 + m2v2 = MV

where, m1 and m2 are the masses of the moving and stationary vehicle, respectively. v1 and v2 are the velocities of moving and stationary vehicle, respectively. M and V are the mass and velocity of the combined mass (consisting of the two vehicles) after the collision. 

Thus, 

1000 x 25 + 1500 x 0 = (1000 + 1500) V = 2500 V

or. V  = (25 x 1000) / 2500 = 10 m/s

Thus, the speed of combined cars, after the collision, is 10 m/s.

Here, we have assumed that the motion is in one-direction only. 

Hope this helps. 

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