Final answer:
The applied force on the skateboard can be found by calculating its acceleration over 1.0 m and using Newton's second law. After the force is removed, the kinetic frictional force that brings it to rest can be calculated using the work-energy principle.
Step-by-step explanation:
To calculate the force applied to the skateboard and the frictional force opposing its motion, we need to analyze the motion in two parts: the acceleration phase and the deceleration phase caused by friction after the force is removed.
Acceleration Phase:
The skateboard accelerates over a distance of 1.0 m in a time of 8.5 s from rest. The acceleration "a" can be found using the equation of motion:
s = ut + (1/2)at2
Substituting the known values (s=1.0 m, u=0, t=8.5 s), and solving for "a" gives a small acceleration due to the long time taken to cover 1.0 m. The force applied can then be calculated using Newton's second law:
F = ma
Deceleration Phase:
After the force is removed, the skateboard coasts and comes to rest after traveling an additional 1.25 m. The deceleration "a'" is due to the kinetic frictional force. We use the work-energy principle:
Work done by friction = Change in kinetic energy
The kinetic energy at the point where the force is removed is equal to the work done by the applied force. We know the distance decelerated (1.25 m) and that the final velocity is zero. Using the work-energy principle and the equation for kinetic energy (1/2 * m * v2), we can find the kinetic frictional force.
To fully answer the question, one would need to follow the steps above with the specified values, calculating "a" and then "F", followed by calculating the deceleration "a'" and using it to find the frictional force, "f".