For example, a car hits a brick wall. But the car was traveling at constant speed. Zero acceleration.
In: Physics
You are confusing momentum (p=mv) with force (f=ma). The relationship between the two can be seen with the impulse. Change in momentum, delta_p = mass.x.delta_v (change in velocity). Divide both sides by change in time, delta_p/delta_t = mass.x.delta_v/delta_t. The right side of the equation can be rewritten as mass.x.acceleration (delta_v/delta_t = a). Bringing it all together, this means delta_p/delta_t = ma = f, or rewritten delta_p = f.x.delta_t ([Wikipedia – impulse physics definition](https://en.m.wikipedia.org/wiki/Impulse_(physics)))
In plain english, this equation just says that the change in the momentum of an object can be established by a force applied externally for a period of time. In this case the brick wall applies a stopping force upon contact. However, it’s not instantaneous, as that would mean the period of time would be 0, and the force would be infinite.
To reduce the force felt from the impact by the passengers, vehicle manufacturers add crumple zones (aka bumpers). They increase the time it takes for momentum of the car to decrease to zero, and thereby reduces the force felt.
Edit~ sorry about the formatting for the first paragraph.
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