The graph below shows the position (km) vs time (s) of an object that is dropped, from rest, from a height of 3 km. Air resistance is present during the fall. The dashed parabola shows what the path would be if air resistance was not present (i.e. free fall) and the dashed line shows the long-term behavior of the object. Assume positive is up and negative is down and that this takes place on Earth.
a) Calculate the velocity that the object asymptotically approaches as it falls by finding the slope of the dashed line. Give your answer in km/s.
b) Make a rough sketch of the velocity vs time graph for the falling object. Include the velocity analogues of the dashed curves.
c) What is the acceleration at t = 0 s? As the object falls, what does the acceleration asymptotically approach?
d) Make a rough sketch of the acceleration vs time graph. Include the acceleration analogues of the dashed curves.
Position (m)
3.5
3.0
2.5
2.0
1.6
1.0
0.6
1.0
2.0
Time (s)
40
30
20
10
0