Question

A 2000 kg car is sitting at a stop sign and begins to accelerate to a speed of 5km/hr at that moment a 1000kg car smashed into the rear end of thus car and stuck together in the collision. A cop shows up to the scene and assumes the 1000 kg car was speeding at 50km/hr by measuring the tire marks that are 3 m long. Assume the the coefficient of friction is 0.8 what is the speed that the car was going when the accident took place.

Answer 1

The frictional force is given by where N is the normal force

After the two cars are stuck together, where m_1 and m_2 are the masses of the two cars

Therefore

The deceleration due to this force on the combined system of the two cars is

Substituting the value of the coefficient of friction

deceleration is

Let the initial velocity of the combined two-car system right after the collision be

Based on the tire marks, it came to rest after a displacement of and

Since acceleration is opposite to the direction of motion, it is negative

Use Newton's equation of motion

Substituting values

Therefore

Converting units,

This is the speed of the combined two car system right after the collision

Since momentum is conserved even in an inelastic collision, we have the momentum conservation equation

where v_1 and v_2 are the velocities of the two cars right before the collision

We know m_1 had a speed of v_1=5km/hr right before the collision.

Putting this back to the equation

Rearranging,

Therefore, the 1000kg car was speeding at 64.1km/hr when the accident took place