Final answer:
To determine how far the truck slides before stopping, we use the equation for kinetic energy and work related to friction. After substituting known values into the simplified equation, the calculated stopping distance is 46.86 meters, which doesn't match any of the provided options, suggesting a possible error in the question.
Step-by-step explanation:
To calculate how far the truck slides before stopping, we need to use the equation for kinetic energy and work. The work done by the frictional force is equal to the change in kinetic energy of the truck. This can be calculated using the following equation:
Work done by friction = Kinetic Energy
Since the work done by friction (Work) is also equal to the force of friction multiplied by the distance (d), and the kinetic energy (KE) of the truck is ½mv² where m is mass, v is velocity and the force of friction is μN, where μ is the coefficient of friction and N is the normal force (N = mg, with g being the acceleration due to gravity), we have:
μmgd = ½mv²
The mass (m) can be canceled out on both sides, which simplifies the equation to:
μgd = ½v²
Solving for d gives us:
d = ½v² / μg
Plugging in the given values (μ = 0.68, g = 9.81 m/s², v = 25 m/s), we get:
d = ½(25 m/s)² / (0.68 * 9.81 m/s²)
d = 312.5 / 6.6708
d = 46.86 m
However, none of the provided options match this result. It appears there may have been a miscalculation or an error in the question or the given choices, since 46.86 m is not listed.