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In something like a car crash, why does increasing the amount of time it takes a person to come to a stop reduce the force they experience?

MultiFazed: >In something like a car crash, why does increasing the amount of time it takes a person to come to a stop reduce the force they experience?

Because force is defined as mass multiplied by acceleration, and acceleration is defined as distance divided by time squared. Or, to put that in equation form:

f = m*a

a = d/t^2

So combining the two, you get:

f = (m * d) / t^2

Since time is in the denominator, making it larger makes the force smaller.

AureliusCM: I’m not completely understanding the question since the title and text can be interpreted differently.

The title makes it sound like the vehicle has a longer time to stop. In that case, the force of impact is less. For example in situation A the vehicle has 2 seconds to stop. It gets down to 20 mph in those 2 seconds. In situation B the vehicle had 3 seconds to stop. It gets down to 20 mph in the first 2 seconds and has a whole extra second to slow down further. The impact will then be at a lower speed.

The description sounds like the vehicle takes longer to stop. In that case the force of impact would be greater. We would be comparing two vehicles with different braking rates that have a fixed amount of time to stop. The car that takes a longer time to stop will be at a greater speed at the moment of impact so the impact will have more force.

FinalBosss: Person is not a piece of solid rock (And slower slowdown even works for rocks). Front of your body – skin, muscles, ribcage try to stop, while backside of your body still has the speed. So it all collides, back muscles into backbone, which collides into organs, which collide in ribcage, etc. Which causes G-forces and injury.

By slowing down over longer time, you’re reducing speed and spread the impact force out

Skaffer: Because the longer it takes something to stop, the smaller its acceleration, force is equal to mass times acceleration, thus your force is also smaller.

And if you are talking about the actual impact (momentum), it is a product of velocity (speed) times mass, so if you hit something moving slower, it feels like less.

Good examples, being hit by a bullet, vs having a bullet thrown at you.

Cars typically bend/crumple like an accordion to slow down the speed of the car before coming to a stop, absorbing the initial shock/energy.

avisaxena33: Newton’s 2nd law is force = mass x acceleration.

In other words, force = mass x change in velocity.

This is basically the derivative of momentum, mass x velocity, known as impulse.

Another way of defining impulse is the amount of force applied over a certain time, impulse = F x change in Time.

We know momentum is conserved, so if we increase the time before impact, the amount of force applied at that instant is lowered and vice versa.

Trogluddite: This is tricky! The total force of the impact will actually be about the same if you increase the time before stopping. There are two things we need to think about: instantaneous force, and total force.

There are a few things we need to know about to understand this.

Force: this is anything that will cause a change in motion. It’s like pushing and pulling.

Mass: how much something will *resist* changes in motion when a force is applied. More mass means that you need more force to feel the same change in motion, or that a the same force will cause less change in motion.

Velocity: how fast is something moving?

Acceleration: over time, how much does something’s velocity change? In other words: how much is it speeding up or slowing down?

Impulse: if something is accelerating over time, we know that a force is being applied. If you add up all of the forces over the time that something is accelerating, you know the impulse. In other words: impulse is the total force applied to something in a period of time.

The total amount of force needed to stop a mass at some velocity (the impulse), remains the same no matter how long it takes.

If we spread out the force over a longer amount of time, though, the amount of force at any specific time is smaller. The acceleration is lower when the time is longer.

If we squeeze the force into a smaller amount of time, though, the amount of force at any specific time is larger. The acceleration is higher when the time is shorter.

The acceleration will increase if the time for the impact decreases. The acceleration decreases if the time period is longer.

From this we learn that *acceleration*, not force, is what we need to worry about if we’re thinking about damage in an impact. This is why cars have air bags — the air bag increases the amount of time it takes a person to slow down during an impact, which reduces the acceleration they feel. The force at any instant is lower — but the total force is the same.

**Drone footage of controlled demolition**

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