physics
posted by stephanie .
Calculate the force needed to bring a 1070–kg car to rest from a speed of 89.0 km/h in a distance of 110 m (a fairly typical distance for a nonpanic stop).
2.97×103 N correct answer
Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.34 m. Calculate the force exerted on the car and compare it with the force found in part (a).
Force = 1.40×105 N
Ratio = 47.0
correct answer
what are the steps to get these answers?

force = mass * acceleration
now the kinematics
first units
89 km/h * 1000 meters/km * 1 h/3600 seconds
= 24.7 meters/second
average speed during stop = 24.7/2 = 12.36
so how long did it take?
t = 110 meters/12.36 m/s
= 8.9 seconds to stop
acceleration assumed constant so it is
a = 24.7 m/s / 8.9 s
a = 2.78 m/s^2 (about 1/3 acceleration of gravity)
F = 1070*2.78 = 2975 N
so we agree
Now do all that for 2.34 meters (OUCH!!)
t = 2.34 meters/12.36 m/s
= .1893 seconds
a = 24.7/.1893 =  130 m/s^2
( about 13 times gravity !!! )
F = 1070 * 130 = 139,599 N
139599/2975 = 46.9
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