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in an automobile crash, a vehicle was stopped at a red light is rear-ended by another vehicle. The vehicles have the same mass. If the tire marks show that the two vehicles moved after the collision at 4 m/s, what was the speed of the vehicle before the collision

Respuesta :

8 m/s

Explanation:

Using conservation of momentum :-

[tex]m1u1 + m2v1 = m1u2 + m2v2[/tex]

Where:

m1 = Mass of first vehicle

m2 = Mass of second vehicle

u1 = initial speed of first vehicle

v1 = initial speed of second vehicle

u2 = Final speed of first vehicle

v1 = Final speed of second vehicle

From the received informations:

[tex]m1 = m2[/tex]

[tex]v1 = 0[/tex]

[tex]v2 = u2 = 4 \frac{m}{s} [/tex]

So

[tex]m1u1 + 0 = 4m1 + 4m1[/tex]

Now divide both sides by m1 :-

[tex]u1 = 4 + 4[/tex]

[tex]u1 = 8m/s[/tex]

Therefore, final answer is 8 m/s

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