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.

A force is acting on a 2.00 kg particle whose position changes with time as x = 4.0 t² - (1/3) t³, with x in meters and t in seconds. 8. find the work done on the particle by the force from t = 0 tot 3.0 sec. b. 327 J a. 256 J c. 164 J d. 225 J

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Which of the following statements is NOT true, in regards to force and displacement vectors? (explain why). (a) When they have a 45-degree difference, the most work possible is done. (b) When they have a 180-degree difference, work is negative (c) When they are parallel, positive work is done. (d) When they are perpendicular, no work is done.

A force of F= (263 N)E -(125 Nj acts on an objeut, causing a displacement of Āp =(3.15 m) î + (2.81 m) . %3D What is the work done on the object?

As a segment of an workout regiment to toughen their pectoral muscles, a man stretches a spring which has a spring constant k=605N/m. a) If x=0 corresponds to when the springs are at their relaxed state, which image best represents the magnitude of the force applied to the springs as a function of the stretch distance (see image). b) Write an equation for the work necessary to stretch the spring from the relaxed state to a distance x1. c) Calculate the work, in joules, required to stretch the spring from its relaxed state to the position x1=59.7cm d) Write an equation for the work necessary to stretch the spring from the position x1 to position x2. e)  Calculate the work, in joules, required to stretch the spring from x1=59.7cm to x2=96.8cm.

Figure 9 shows four situations in which a force F is applied to an object resulting in displacement Ař. The force has the same magnitude in all four cases, but points in different directions. The displacement is exactly the same in all four cases. Which of the following choices correctly ranks the work done by the force on the object? a) W. < Wa < Wa < Wp b) Wa < Wc < W, < Wa c) Wa < Wc < Wa < Wp d) Wa < W, < Wa < Wc e) Wh < Wa < Wa < Wc Ar Δ b Ar Ar Figure 9

A 1350-kg car is traveling with an initial speed of 25.0 m/s. Determine the car's speed after -2.20 × 10° J of net work is done on the car. X m/s

The kinetic energy of a system must always be positive or zero. Explain whether this is true for the potential energy of a system.