We can use the conservation of momentum principle to solve this problem. According to this principle, the total momentum of a system of objects remains constant if there are no external forces acting on the system. In this case, we can assume that there are no external forces acting on the two cars after they collide, so the total momentum of the system before the collision must be equal to the total momentum of the system after the collision.
The momentum of an object is defined as its mass multiplied by its velocity:
momentum = mass * velocity
Before the collision, the momentum of the first car (m1) is:
p1 = m1 * v1 = (0.1 kg) * (1.0 m/s) = 0.1 kg⋅m/s
Since the second car is stationary, its momentum before the collision is zero:
p2 = m2 * v2 = (0.15 kg) * (0 m/s) = 0 kg⋅m/s
The total momentum of the system before the collision is:
p1 + p2 = 0.1 kg⋅m/s + 0 kg⋅m/s = 0.1 kg⋅m/s
After the collision, the two cars move together with a common velocity (v), so the momentum of the system is:
p = (m1 + m2) * v
We can set the total momentum before the collision equal to the total momentum after the collision:
p1 + p2 = p
0.1 kg⋅m/s + 0 kg⋅m/s = (0.1 kg + 0.15 kg) * v
0.1 kg⋅m/s = 0.25 kg * v
v = 0.1 kg⋅m/s ÷ 0.25 kg
v = 0.4 m/s
Therefore, the two cars move off together at a speed of 0.4 m/s after the collision.