44.29 g
First, convert 90 km/h into m/s
90 km/h * 1000 m/km = 90000 m/h / 3600 s/h = 25 m/s
So the car decelerated from 25 m/s to 0 m/s over a distance of 0.72 m. The formula for distance under constant acceleration is
d = 1/2 A T^2
The formula for the amount of time taken to decelerate is
T = V/A
Substitute the formula for T into the equation for d, giving
d = 1/2 A (V/A)^2
Substitute the known values of d and V into the formula
0.72 = 1/2 A (25 / A)^2
Solve for A
0.72 = 1/2 A * 625 / A^2 = 1/2 * 625 /A = 312.5/A
0.72 = 312.5/A
Multiply both sides by A
0.72A = 312.5
Divide both sides by 0.72
A = 434.0278 m/s^2
Let's verify A as being correct. T will be 25 m/s divided by A giving
T = 25 m/s / 434.0278 m/s^2 = 0.0576 s
d = 1/2 A T^2 = 0.5 * 434.0278 * 0.0576^2 = 0.72 m
We get the same stopping distance, so we verified that A = 434.0278 m/s^2
Now to convert to "g's"
434.0278 m/s^2 / 9.80 m/s^2 = 44.29 g
