here's why the instructor gave the absolutely great advice:
the original question does not say that someone stops in front of you. here's a true story of an accident i was involved in: i was in a situation where a driver approaching an intersection from the opposite direction as me failed to yield while making a left turn at a green light. i was doing 40mph in a 45 mph zone and traveling straight through the intersection with a green light. when i realized that the other driver was cutting me off, i had 2 reasonable options: swerve to the right to try and avoid the accident and possibly hit another (innocent) vehicle, or lightly apply brakes and steer straight ahead knowing full well that i would hit the other vehicle. my 3rd option was unreasonable as it was to swerve to the left and definitely hit another vehicle and my 4th option was equally unreasonable as it would have been to slam on my (non-ABS) brakes and likely lose control of my vehicle.
as a former car insurance adjuster here's my input: if speed/conditions make an accident unavoidable without complete knowledge that avoidance will not cause you to hit another car or stationary object, you always want to hit the guilty party and avoid at all costs the fatal (to your wallet) mistake of swerving to avoid the guilty party and hitting an innocent party or crashing your car without touching his. if the guilty party's car is unscathed (without even paint transfer to attest to the accident), he can get away free and clear and leave you with the headaches of triple insurance rates for the next 5 years if you hit another vehicle trying to avoid his.
there is also the ethical dilemma in a situation like this: would you rather: potentially injure or kill the at-fault driver, OR potentially injure or kill a completely innocent party?
me, i'll take the 100% chance of hitting the guilty party over even a 1% chance of hitting an innocent party.
you wait until the last second to apply brakes because you don't inadvertently want to lose control and miss the guilty party and possibly strike an innocent party. the only reason to apply brakes at all is you want skid marks to kill his defense that you had the "last clear chance" to avoid the accident.
no judge is going to fault you for an accident for failing to swerve. as long as you have proof (skidmarks) that you made any attempt (however small) to avoid the accident, you are free and clear.
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now on to the physics side of the dilemma: hit the side of a barn going 10 miles per hour and the car will suffer more damage than the barn. hit the side of a barn going 100 mph and the barn will suffer more damage than the car. OR, fire a .500 inch round 100% lead ball from a muzzle loading rifle with a max charge of approx 120 grains fff black powder (a typical deer hunting load). fire this into a .500 inch thick plate of 100% lead. the bullet will pass through the lead plate relatively intact while the plate will have a nice, round hole in it. bullet's momentum/inertia due to it's mass * velocity will cause it to "win" this contest - it has more inertia to keep going than the lead it displaces has to remain static.
another way to look at it. say my 5000lb truck traveling at a rate of 30 mph hits the back of a fully loaded stationary 80000lb dumptruck. the dumptruck's inertia to stay at rest will cause it to move very slightly with most of the forces of the crash being absorbed by my truck and causing injury to myself and my truck. but what if i rear-end a 2000 lb stationary compact car at the same speed? my inertia to keep moving is a lot more than the car's inertia to stay at rest. the car will absorb most of the damage and my i will likely be able to drive my truck away from the accident.
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from a traffic law precidence/automotive accident claims standpoint, the instructor's advice is good and is exactly what i have recommended to friends/family if they find themself in the same situation.
from a physics standpoint, the vehicle with the most momentum "wins" and will be less likely to be damaged and more likely to transfer the impact (damage) to the vehicle with the lesser momentum.
it shouldn't take a history/philosophy major to figure this out, folks. put the calculators down and go experience some real, everyday, living. then read some plato. how smart people can be so single-minded totally blows my mind. the speed of one vehicle at the time of impact was all that was being considered on this thread. i can see ya'll missing the legalistic aspect of it, but the moral one? and, as to physics, an intact drinking straw imbedded 3 inches into a telephone pole during a hurricaine will testify that mass*velocity is the key to it all. the object with the most momentum whether by a high mass, a high velocity, or both, usually wins the collision game.