[Physics] Bidirectional jerk motion on a stopping vehicle

accelerationforcesinertiajerknewtonian-mechanics

A stopping vehicle (say a car) has an apparent retardation (which may/may not be constant in magnitude) when force via brakes is applied.

I travel by subway trains, and I noticed an odd phenomenon. The thing about such trains (might be irrelevant) is that, being light-weight, their motion somewhat mimics that of cars, and the effects of motion are more apparent as one usually stands in such trains. The thing I noticed was that I could feel a force pulling me in the initial direction of motion, as the train slowed down. That obviously is the inertia. But as soon as the train halted, I noticed a secondary jerk…this time in the opposite direction, and it was kind of short lasting.

I'm curious to know, what causes this secondary jerk backwards as soon as a vehicle comes to rest. I'm guessing it has something to do with the reaction force by the brakes which overcome the forward motion and provide an impulse backwards. But then it has to have a proper force 'mirror' as per the third law of motion. Also, there never is any intentional backwards motion here (the drivers are precise, I guess).

So what could it really be?

Best Answer

I have noticed this effect often in cars and sometimes in trains. This is the reason I think it happens though I can't claim to have done any research.

The car stops because the breaks are applied, the wheels stop turning and there is a force of static friction between the road and the tires. In the car frame of reference I experience this backwards acceleration of the car as a forwards (inertial) force on me.

The reason I then feel a secondary force backwards must be because the car has a short acceleration forwards near the end of its stopping. I assume this is because, as it stops, there is some energy stored as elastic potential energy in the tires and/or the suspension system. Once the car is finished moving forwards this stored elastic energy causes it to "spring back" a bit right at the end.

Subway trains don't usually have rubber tires (though they do in Montreal) but the do have some sort of sprung suspensions system that could act in a similar way.