# Math Help - Car crash, Seatbetls, impulse

1. ## Car crash, Seatbetls, impulse

Also ive been trying to get my head around an equation for seatbelts. Hyperphysics has an auto calculator and ive been trying to do it algebraically and still cannot get the same answer.

Here is what i have done...

In relation to a car travelling at 50mph with a driver which weighs 75kg and stops with in 1 foot.
Car Crash Example

m = 75 kg, initially travelling at 50kmph = 13.88888889m/s d= 30 cm
Distance time interval =
dt = 0.3 m / 13.88888889 m/s = 0.022 s

During this 220th’s of a second it is decelerated from 13.88888889 m/s to zero, so
a = dv/dt = 13.88888889 m/s / 0.022 s = 631 m/s^2

So the impact force is
F = m x a = 75 kg x 631 m/s^2 = 47348N ....

But it is completely different answer

2. Originally Posted by Dingo
Also ive been trying to get my head around an equation for seatbelts. Hyperphysics has an auto calculator and ive been trying to do it algebraically and still cannot get the same answer.

Here is what i have done...

In relation to a car travelling at 50mph with a driver which weighs 75kg and stops with in 1 foot.
Car Crash Example

m = 75 kg, initially travelling at 50kmph = 13.88888889m/s d= 30 cm
Distance time interval =
dt = 0.3 m / 13.88888889 m/s = 0.022 s

During this 220th’s of a second it is decelerated from 13.88888889 m/s to zero, so
a = dv/dt = 13.88888889 m/s / 0.022 s = 631 m/s^2

So the impact force is
F = m x a = 75 kg x 631 m/s^2 = 47348N ....

But it is completely different answer

3. Originally Posted by skeeter
How?
or how else should i calculate it?

4. $v_f^2 = v_0^2 + 2ad$

5. Originally Posted by skeeter
$v_f^2 = v_0^2 + 2ad$
Where Vf and V0 represent?
and what forumla is this?

6. Originally Posted by Dingo
Where Vf and V0 represent?
and what forumla is this?
$v_f$ is final velocity ... 0

$v_0$ is initial velocity ... 50 kph

this is the well-known "no time" kinematics equation.

7. I get to.... Ive been working on this all night and now swear im brain dead...

0 = 192.9 + 2*A*0.3

do i...
0 =192.9 + 2*A*0.3 -2*A*0.3
- 2*A*0.3 = 192.9
-2*A*0.3/0.3 = 192.9/0.3
-2*A = 643

-2*A/-2*A = 643/-2*A
0 = 643 / -2*A/A
0/A = 643 /-2
A = 643/-2

A = 643 / -2
A = 321.5 ms^2 (- Negative due to deceleration...

8. 50 kph = 125/9 m/s

1 ft = .3048 m

0 = (125/9)^2 + 2a(.3048)

a = -(125/9)^2 / [2(.3048)] = -316.439 m/s^2