Question

in an automobile crash, a vehicle that 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

Answer 1

The initial speed of the vehicle before the collision is 8 m/s.

• Let the mass of the vehicle = m
• Let the initial speed of the vehicle stopped = u
• The initial speed of the vehicle parked at the red light = 0

Principle of conservation of linear momentum

• The initial speed of the vehicle before the collision is calculated by applying principle of conservation of linear momentum as follows;

$m_1 u_1 + m_2 u_2 = v(m_1 + m_2)\\\\mu + m(0) = 4(m+ m)\\\\mu = 4(2m)\\\\mu = 8m\\\\u = 8 \ m/s$

Thus, the initial speed of the vehicle before the collision is 8 m/s.

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