Question

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

Answer 1

8 m/s

Explanation:

Using conservation of momentum :-

$m1u1 + m2v1 = m1u2 + m2v2$

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:

$m1 = m2$

$v1 = 0$

$v2 = u2 = 4 \frac{m}{s}$

So

$m1u1 + 0 = 4m1 + 4m1$

Now divide both sides by m1 :-

$u1 = 4 + 4$

$u1 = 8m/s$

Therefore, final answer is 8 m/s