You have arrived at the scene of a two car accident. You know the following pieces of information:

Car 1 and car 2 have equal masses of 2,000 kg each

Car 1’s initial momentum was 40,000 kg-m/s to the right; Car 2 wasn’t moving

Car 1 collided with car 2

Car 1’s final velocity is 10 m/s to the right; car 2’s final velocity is unknown.

What is each cars initial velocity

We can solve the problem by using the law of conservation of momentum: the total momentum of the system must be conserved before and after the collision.

Therefore, we can write:

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]

where:

[tex]m_1 = 2000 kg[/tex] is the mass of the first car

[tex]u_1[/tex] is the initial velocity of the first car

[tex]v_1 = 10 m/s[/tex] is the final velocity of the first car (taking right as positive direction)

[tex]m_2 = 2000 kg[/tex] is the mass of the second car

[tex]u_2 = 0[/tex] is the initial velocity of the second car

[tex]v_2[/tex] is the final velocity of the second car

We also know the initial momentum of car 1, which is

[tex]p_1 =40,000 kg m/s[/tex]

And since momentum is the mass times the velocity, we find the initial velocity of car 1:

[tex]u_1 = \frac{p_1}{m_1}=\frac{40,000}{2,000}=20 m/s[/tex]

with a positive sign, since the direction is to the right.

Now we can re-arrange the previous equation and solve for v2, the final velocity of car 2:

[tex]v_2 = \frac{m_1 u_1 -m_1 v_1}{m_2} = \frac{(2000)(20)-(2000)(10)}{2000}=10 m/s[/tex]

And since the sign is positive, the direction is the same as the initial direction of car 1, so to the right.

Learn more about momentum here:

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