Question

During a demolition derby, vehicle 1 collided vehicle 2 going in the opposite direction and came to an immediate stop. If the vehicles are of different masses and were not travelling at the same velocity, what can be concluded about them? *

Answer 1

Answer:

The change in momentum of the two cars is equal and opposite

Explanation:

The change in momentum of an object is given by:

$\Delta p = m\Delta v$

where

m is the mass of the object

$\Delta v$ is the change in velocity

According to Newton Laws of motion, the force experienced by an object is equal to the rate of change of its momentum:

$F=\frac{\Delta p}{\Delta t}$ (1)

where

$\Delta t$ is the time interval during which the force is applied.

According to Newton's third law of motion, the force exerted by vehicle 1 on vehicle 2 during the collision is equal and opposite to the force exerted by vehicle 2 on vehicle 1. Therefore, we can write:

$F_1=-F_2$

Using (1), we can rewrite this as:

$\frac{\Delta p_1}{\Delta t}=-\frac{\Delta p_2}{\Delta t}$

Where $\Delta p_1, \Delta p_2$ are the changes in momentum of car 1 and 2, and $\Delta t$ is the duration of the collision. Simplifying, we get

$\Delta p_1 =-\Delta p_2$

So, the change in momentum of the two cars is equal and opposite.