# Help Need to calculate deceleration of object crashing

• tcdesignguy

#### tcdesignguy

Hello,

Running a FEA on a object and need to calculate the deceleration from 5mph to 0mph and 10mph to 0mph . The vehicle weight is 2935lbs. They ran one test and said the vehicle stopped after it crumpled just less than 1". (I assume we can use the distance and velocities to solve the time?? (How long it took to stop from 5-0 in less than 1"))

So if i understand right we want to solve for t not a.

-Steve Campbell

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Welcome to PF.

The formula to use is $$v^2 = 2 a d,$$ where v is the speed, a is the deceleration, and d is the distance. Solving that for the deceleration a gives $$a = \frac{v^2}{2d}$$

You can https://www.google.com/#sclient=psy...,cf.osb&fp=7de1449e07857063&biw=1280&bih=607" to calculate the deceleration from that formula.

Or if you want to do things the hard way, then keep reading...

The units are tricky here! We have both miles and inches in the mixed in the mix, and I don't know what units you like to use for acceleration or deceleration -- I will use mph/sec as that seems convenient.

To make the units work out, first convert v into inches per second:
$$5 \ mi/hr \cdot \frac{12 \cdot 5280 \ inches}{1 \ mile}\cdot \frac{1 \ hr}{3600 \ sec}= \frac{5 \cdot 12 \cdot 5280}{3600} \frac{mi}{sec}= 88 \ in/sec$$

(Or https://www.google.com/#sclient=psy...,cf.osb&fp=7de1449e07857063&biw=1280&bih=607" to do the conversion for you.)

So the deceleration is $$a = \frac{v^2}{2d} = \frac{5 \ mph \cdot 88 \ in/sec}{2 \cdot 1 \ in} = 220 \ mph/sec$$

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