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I'm trying to answer the question below, and I'm struggling to understand what the question means by a constant force throughout a collision. The mark scheme states that a constant force will mean that the force will be lower. I can answer the rest of the question from that point on, but I'm struggling to fill in this gap.

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We know the driver initially has a momentum $mv$, where $m$ is the driver's mass and $v$ is the velocity of the car. After the crash the driver's momentum is zero, so the momentum has changed by $mv$.

If the force decelerating the drive is $F(t)$, where I've made the force a function of time to indicate that it may change with time, then the change of the driver's momentum is related to the force and the duration of the collision, $T$, by:

$$ \Delta p = mv = \int_0^\text{T} F(t)\,dt $$

Or if we look at this graphically rather than using an equation, then if we draw a graph of the force as a function of time then the momentum change is the area under the curve from $t=0$ to $t=T$.

Given that the change in momentum $\Delta p = mv$ is outside the seat belt designer's control, the question is asking you how best to design the seatbelt so as to limit the maximum force that the driver experiences.

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  • $\begingroup$ I think I understand now. If the area under the graph is the change in momentum and we have a constant force for a longer period of time, then the graph has been stretched, to account for a constant force for a period, so the highest force has been reduced. $\endgroup$ – Andrew Brick Nov 27 '16 at 12:04
  • $\begingroup$ Exactly, you got it. $\endgroup$ – Pirx Nov 27 '16 at 15:29

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