An uncontrolled 850 kg car strikes squarely a motorway crash cushion in which the car is brought to rest by successively crushing steel barrels. The length of the crash cushion is 5.9 m, and the magnitude F of the force required to crush the barrels as a function of the distance the car has moved into the cushion is given by (image attached) a) Determine an expression for the work done by the force Fas a function of x b) If the car strikes the crash cushion with a velocity of 38km / h , determine the distance the car will move into the cushion before it comes to rest and the maximum deceleration of the car. c) Determine the maximum velocity with which the car can strike the cushion so that it will not hit the wall behind the cushion.

An uncontrolled 850 kg car strikes squarely a motorway crash cushion in which the car is brought to rest by successively crushing steel barrels. The length of the crash cushion is 5.9 m, and the magnitude F of the force required to crush the barrels as a function of the distance the car has moved into the cushion is given by (image attached) a) Determine an expression for the work done by the force Fas a function of x b) If the car strikes the crash cushion with a velocity of 38km / h , determine the distance the car will move into the cushion before it comes to rest and the maximum deceleration of the car. c) Determine the maximum velocity with which the car can strike the cushion so that it will not hit the wall behind the cushion.

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