A car of mass 1500 kg traveling at 15.6 m/s loses its brakes and collides with the rear end of the car in front of it, which has a mass of 1020 kg and is traveling in the same direction at 12.5 m/s. If the smaller car is given a speed of 15.3 m/s by the collision, what is the speed of the larger car after the collision?

M1*V1 + M2*V2 = M1*V3 + M2*V4.

1500*15.6 + 1020*12.5=1500*V3+1020*15.3
23,400 + 12,750 = 1500V3 + 15,606.
36,150 = 1500V3 + 15,606.
1500V3 = 20,544.
V3 = 13.7 m/s.

To find the speed of the larger car after the collision, we can use the principle of conservation of linear momentum. This principle states that the total momentum of an isolated system remains constant before and after a collision.

The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum of the larger car before the collision can be calculated as:

Momentum (before) = mass (larger car) * velocity (larger car) = 1500 kg * 15.6 m/s

Similarly, the momentum of the smaller car before the collision is:

Momentum (before) = mass (smaller car) * velocity (smaller car) = 1020 kg * 12.5 m/s

According to the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore:

Momentum (before) = Momentum (after)

1500 kg * 15.6 m/s + 1020 kg * 12.5 m/s = mass (larger car) * velocity (larger car) + mass (smaller car) * velocity (smaller car)

We know the mass and velocity of the smaller car after the collision, which is given as 15.3 m/s. Let's substitute the values into the equation:

1500 kg * 15.6 m/s + 1020 kg * 12.5 m/s = mass (larger car) * velocity (larger car) + 1020 kg * 15.3 m/s

Now we need to solve for the velocity of the larger car.

(1500 kg * 15.6 m/s + 1020 kg * 12.5 m/s - 1020 kg * 15.3 m/s) / mass (larger car) = velocity (larger car)

By plugging in the values, we can calculate the velocity of the larger car after the collision.