An uncontrolled 1000kg automobile strikes squarely a motorwa

An uncontrolled 1000kg automobile strikes squarely a motorway crash cushion of the type shown in which the automobile is brought to rest by successively crushing steel barrels. The length of the crash cushion is 6m, and the magnitude F of the force required to crush the barrels as a function of the distance x the automobile has moved into the cushion is given by

If the automobile strikes the crash cushion with a velocity of 100km/h, determine the distance the automobile will move into the cushion before it comes to rest.

Solution

The length of the crash cushion is 6m, and the magnitude F of the force required to crush the barrels as a function of the distance x the automobile has moved into the cushion is given by

the distance will be   Force = mass * acelaeration

aceleration = 160 kN / 1000 kg = 0.16 m / s^2

aceleration = velocity / time

time = 100 km/hr * ( 1 hour / 60 min ) / 160 = 0.01042 sec

Distance = 100 * ( 1 / 60 ) / 0.01042 = 159.95 meters